Chiken Emojis & Symbols

⣀⣠⡅⠀⠀⠂⢀⡀
⡟⠛⢡⣼⡄⣼⡏
⢦⡜⠓⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⢸⣿⡆
⠘⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣄⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⣻⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠻⣿⣧⡀⠀⠀⢠⣿⡄⠀⠀⠀⢸⣿⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣀⠿⠷⠀⠀⠈⠿⠃⠀⠀⠀⣨⣿⠀⠀⠀⢀⣿⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠀⠀⢠⣾⣿⠀⢰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠋⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠄⡀⠀⠀⠀⠠⠄⠋⠉⠀⠀⠐⠲⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠸⠗⠀⠀⠘⠀⠀⠀⠀⠄⠈⠂⠂⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡦⠂⣀⣀⡿⣶⣦⠹⣶⢀⠀⠀⠀⠀⠀⢄⡀⠀⢀⠀⠆⠈⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⠠⠄⠀⠈⢿⣀⡘⡤⡦⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡄⠆⢠⡄⠀⠉⠻⠇⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠛⠉⣟⣻⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣧⣶⠀⠀⠀⠀⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣦⣄⠀⢸⣿⣿⣿⠸⣿⢻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⡀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡟⣿⣾⣿⣿⣿⡿⠀⠙⠻⢿⣿⣷⣾⣿⣻⣿⣿⣿⣿⣬⣉⣼⣿⣿⣿⠟⢀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⣠⣶⣿⣟⣿⣿⣿⢻⣷⠸⣿⣿⣿⡟⠀⠀⠀⢀⣀⣠⣿⣿⣿⡿⡿⢿⣿⣿⣽⣿⡟⣩⣵⣿⠀⢸⣯⡿
⠀⠀⠀⢀⣤⣾⣿⣿⠿⢋⣿⣿⡏⣸⣿⡆⠘⣿⣿⣿⣾⣿⣿⣿⣿⣿⣍⠛⣋⣭⣵⣶⣿⣧⣤⣿⢿⣯⣿⣭⣧⣾⡟⠁
⠀⢀⣴⣿⣿⣿⠟⢀⠴⣻⣿⣿⣇⠹⢿⠟⠀⣿⣿⣿⣿⣿⣧⡿⠿⠿⢿⣿⣷⣿⣼⣏⠉⠛⠯⣍⠀⠈⠉⠈⣿⣿
⣴⣿⣿⣿⡿⠏⢀⠓⢈⣿⣿⣿⣿⣿⣶⣄⠀⣼⣿⣿⣿⡿⣉⣤⣾⣿⣷⣿⠿⣡⣦⣿⠂⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆
⣿⣿⣻⠟⠁⠄⠃⣰⡟⣱⢟⣿⢿⣿⣿⣿⡄⣿⣿⠟⣉⣴⠋⣼⣿⣿⣿⣿⣄⣼⣿⠛⣿⣷⣶⣄⡀⠀⠀⠀⠀⢿⡇
⣿⢷⡟⠁⠀⢠⡾⢫⠘⣁⠋⠀⢈⣿⣿⣿⣿⡟⢡⣿⣿⢁⠈⣿⣿⣿⡾⠁⠛⢿⣿⣆⢹⣿⣿⣿⣿⠑⠒⠦⢄⣘⡇
⠻⠆⠀⢀⡼⢋⡔⠃⠀⢀⡞⠀⢸⡇⢸⣿⡿⢡⣿⣿⣯⣾⢠⣿⣿⣿⣷⣈⣧⡾⣿⡿⠂⣿⣿⣿⣿⣿⣦⡄
⠁⢀⠀⠉⢠⠊⠠⠀⣠⣿⠂⠀⠏⡇⣸⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⡇⣼⠟⢻⡗⠛⣿⣿⣇
⠀⠀⠀⠀⠁⠠⠀⣴⠛⠏⠀⢠⢰⡇⣿⣿⠀⠹⣿⣿⣿⣟⡿⠉⠈⣿⣿⣿⣿⣹⡿⣱⣿⣿⡟⠁⠀⠙⠿⠸⡀
⠀⠀⠀⠀⠀⠀⠸⠃⢺⠀⠀⠀⢈⢀⣿⣿⣷⣀⠛⠿⣿⡟⠁⠀⠀⠀⣿⣿⣿⢹⣷⣿⣿⡿⣟⡀⠀⠀⠘⢶⡇
⢠⡎⠀⠈⠀⠂⠀⠀⠘⠀⠀⠀⠀⡼⢯⢹⣿⣿⣷⣤⡘⡌⠀⠀⠀⣸⣿⣿⣿⣿⣽⣿⣿⣷⣿⣧⠀⠀⠀⡼
⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⣿⢱⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠸⣿⣿⣿⠧⢼⣿⣿⣿⣿⣿⠀⠀⢐⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣤⣸⣿⡿⣎⣃⣼⢿⣿⣿⠟⢡⠂⣠⠎
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢰⣇⣀⣿⣿⣿⡿⣿⣇⢡⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣫⣟⣚⠿⠄⣃⣠⡟⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡟⢹⣿⣯⣿⣿⣿⣧⣾⢻⣿⣏⣿⣿⣿⣿⣿⣿⣿⠋⠈⠀⡡⢴⣵⠟
⠀⡀⠀⠀⠀⢠⣿⠀⣿⣻⣷⣿⣧⢿⣿⣿⣿⡿⣠⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣩⣴⠟⠁
⠀⠁⡄⢰⢀⡿⣿⠀⣷⣾⣧⣿⣿⣾⣿⣿⣿⣟⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿
⢀⡄⣵⣾⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⡗⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣇⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⠀⣿⢿⣿⣿⣿⣟⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡄
⠈⠠⣿⣼⣯⣾⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣸⣿⠇⣻⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠢⣄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠊⠁⠈⡆
⠀⠀⠀⠀⢠⠒⠀⠒⠾⠀⠀⠈⠂⠀⢄⠀⠓⠂⢄
⠀⠀⠀⠀⢠⠀⠀⠠⠀⣀⠀⠀⠘⠃⠀⠤⠒⡄⡸
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠈⠢⡀⠢⡀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣐⣀⠔⠂⠀⠘⠺⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⠀⠤⠀⢁⠀⢀⠴⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⣀⠀⠀⠀⠀⠶⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠘⢾⠀⠀⡆⢸⡰⠋⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠛⠱⡎⠉⢙⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠂⢄⡘⠀⢠⢘⠔⠁⡀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠜⠤⠜⠑⡄⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠁⠀⠘⠃⠀⠐⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠦⠤⠤⠒⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠜⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⡇
⠀⠀⠀⠀⠀⢀⠴⠊⢉⣀⡠⠤⢄⠀⠀⢀⡔⢤⡀⠜⠀⢀⠔⡁⠉⠑⠢⠤⠄⠀⠠⠄⠴⠒⡋⠀⠀⠀⠠⠀⡆
⠀⠀⠀⢀⠞⠁⠀⠀⠈⠁⠀⠀⠀⠑⠒⠊⠀⠀⠀⠀⡰⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠢⠂⠀⠀⡇
⠀⠀⠀⡎⠀⠀⠀⠀⠘⠀⠐⠐⠀⠀⠐⠂⠀⠀⠀⠰⠁⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠈⠀⠇
⠀⠀⠀⠱⣀⠀⠀⠀⠀⡇⠀⠀⠈⠊⠀⠀⠀⠉⠀⠠⡀⠀⠉⣠⡄⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸
⠀⠀⠀⠀⢠⠃⠀⠀⠀⢰⠈⠁⠀⠀⠀⠉⠀⠈⠂⠀⠈⠉⠉⠀⡇⢁⠀⠀⡠⢂⠑⠀⠤⠂⡘⠀⠀⠀⠀⡎
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⡆⠀⠀⠈⠀⠀⠂⠀⠀⢀⠀⡀⠀⠀⢣⡀⠁⠀⣠⠊⠑⠦⠀⠊⠀⠀⠐⠁⢰⠁
⠀⠀⠀⠀⠑⠤⠤⢤⠀⠀⠘⣄⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠈⣦⡀⠀⠀⠀⡠⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣀⠀⠀⠀⢀⡴⠁
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠋⠁⠙⠦⣀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠠⠠⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⣄⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠔⠊⠁
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡏⠉⠉⠉⢹⠀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠇⠀⠀⠀⢸⢠⠁
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⣁⣳⣄⣀⣤⣾⢘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠸⠁⠉⠉⠁⠸⠎⠙⠁
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⢤⣾⣭⣓⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⠿⠿⣿⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⢠⡶⡄⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⣠⢞⣉⡉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡙⢷⣿⡇⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⠀⣠⣿⣶⣶⣿⠳⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣦⣿⣷⡀⠹⣿⡄⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⣿⣿⡿⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣌⠻⣿⣷⡀⠹⣿⡘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠠⠀⠀⠀⡀⠀⠈⣻⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠰⣿⡙⠻⢿⣿⣦⡈⠻⣿⣄⠹⣷⡜⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠐⠀⡀⠈⠠⢄⡀⠁⠶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠛⣿⣿⣆⠙⢿⣧⣙⣿⡞⠶⠄⠀⠄⠀⠠⠄⠀⠈⠁⠀⠐⠂⠀⠀⣡⣤⠀⣸⢿⣿⣾⣽⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣙⣿⡿⣦⡀⠻⢿⣷⣮⣿⡏⠉⠓⠀⣀⠀⠀⠀⢤⡀⠀⠘⠓⠀⢀⣸⣶⠞⠙⣿⣿⣧⣟⣸⢋⡿⣿⠁
⠀⠀⠀⠀⠀⠀⠈⣿⣦⡉⠙⠿⢿⣿⣶⣌⡻⣯⠈⠙⢲⡶⠄⠙⠒⠀⠀⣴⠀⠀⠈⣳⠞⠋⣻⡿⣴⡞⢁⡼⠛⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⣳⣤⣀⠉⠙⢿⣿⡟⠳⢤⣀⣙⣦⣄⣀⣀⠒⢺⡿⠛⣛⣻⣷⡞⠁⣈⡼⡻⣿⣧⣞⣠⡟⡽⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣷⣿⣿⣶⣤⣈⠻⢦⡀⠽⣧⣀⠈⠉⠉⣙⣻⣦⣤⡤⠖⢛⣿⣿⡏⢀⡴⠋⣻⠿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⣍⡙⠛⢿⢿⣿⣷⣿⣿⣿⡛⠛⠓⠶⠶⠶⠾⢯⣀⣠⡤⠞⡻⢿⣿⣤⣾⢁⣴⢋⡿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣶⣦⣤⣭⣉⣛⣻⣿⣷⣦⣤⣌⣉⣙⣻⣿⣯⣀⣤⡖⠋⢘⡿⣿⣿⣿⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣷⣴⣏⣘⣹⣃⣋⣿⣥⣾⠋⢙⣽⢶⣶⣏⣠⡞⣩⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣿⣧⣼⣏⣩⡟⠹⣿⠁⣩⣿⢶⣿⣁⣨⡟⢛⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣟⣻⡟⢻⡟⠛⣿⣁⣠⡿⠛⣿⣷⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣛⣿⣁⣼⣷⡾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠿⠿⠿⠿⠻⣯⠾⣿⠷⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠙⣿⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠠⠴⢦⣤⠀⠘⢷⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡏⣩⣤⣄⡍⡍⠨⡿⡅⠀⠈⡷⠂⠀⢤⢴⣤⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠒⠚⠁⠀⠐⠒⠒⠐⣿⢞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⢄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣾⡿⠷⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣓⣈⡐⢆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢰⣿⣿⣯⣿⠗
⠀⠀⠀⠀⣠⣤⣶⣶⣿⣿⣷⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠘⣿⣿⣿⣟
⠀⠐⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠳⡭⠊
⠀⢚⣿⣿⣿⣿⣿⣿⣿⣛⢻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣰⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑
⢿⣿⣿⠁⢻⣿⣿⣿⣿⣧⣤⣔⡰⠻⣿⢛⣛⠀⠀⠀⠀⢀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣯⢉⣿⣿⠃⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠈⠃⠀⣸⣿⣿⣿⣿⣿⣿⣿⣽⣿⢟⡿⡟⠀⠈⠀⠂⠀⡀⠂⠄⠀⢄⠀⠀⠀⠀⠀⠀⠛⡠⣼⠇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠁⣾⡄⢠⢤⣾⡇⢠⡴⡎⣿⣥⣺⢄⣠⣰⠆⣃⣬⠁
⠀⠀⠀⠀⢻⣿⠿⢿⡿⠟⣿⣿⣿⣿⣿⣿⡊⢁⣳⣿⣿⡟⣟⠸⢷⣧⣽⣷⢟⢫⡩⠼⢫⣴⠟
⠀⠀⠀⠀⠀⠻⠀⠀⢧⠀⠾⠋⢹⣿⣿⣴⣳⣿⣿⣿⣃⠀⠈⡷⢾⣯⣻⣛⣛⢁⡀⢖⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠹⠿⣿⣿⣿⡿⢓⣤⢞⣡⠄⢀⣹⣻⡋⣀⢡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣟⡻⣝⣚⣭⣷⣾⣿⣿⣿⣿⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠊⢳⣄⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡄⠀⠑⣾⠀⠀⢋⣿⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠾⠟⠒⠦⠤⠾⠁⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣦⠀⡰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠺⠀⠷⠁⣧⢺⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⣆⠀⠀⠀⠁⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣋⠀⠀⠈⠳⣤⡀⠀⠀⢠
⠀⠀⠀⠀⠀⡎⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠐⢻⣯⠀⠈⠰⣶⠆⢉⡷⠒⢇
⠀⠀⠀⢀⣀⣱⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢉⣧⠀⠀⠠⠠⣀⡼⠧⣤⢤
⠀⢀⣄⢸⠀⠙⢧⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠚⠹⣧⡄⠀⣰⠁⠀⠀⣿
⠀⢸⡌⠳⣇⠀⠈⢣⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠋⣴⣠⣟⠓⠶⠞⠁
⠀⠀⢣⠀⠙⠂⠀⠀⢳⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢹
⢸⠁⠈⠁⠀⠀⠀⠀⠀⠻⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⣇⣸⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠇
⠈⢆⠀⠀⠀⠠⠀⠀⠀⠀⠹⡖⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⠁⠀⠀⠀⠿⠁⣧⠋⡇⠀⣠⠀⠀⠀⠀⢸
⡤⣌⣆⠀⠀⠀⠀⠀⠀⠀⣖⡛⢦⣘⠢⠤⠤⠤⢶⣔⡒⠂⠴⠤⠤⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠚⢹⣀⣤⡀⠀⡆
⠱⡀⠙⢧⡀⠀⠀⠀⠀⠰⣂⠛⠶⢬⠓⠀⠀⠀⠀⠀⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢘⡇⠀⣆
⠀⠙⣄⠀⠳⣄⠀⠀⠀⠀⢠⡛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⢨⠷⣆⡾
⣄⠴⠾⢦⡀⠈⠀⠀⠀⠀⠀⡬⣟⣛⣛⣥⠀⠀⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⣩⠽⠶⠷⢦⡀⠀⠀⠀⠀⠀⠙⠉⠉⠈⠉⠁⠉⠀⠀⠀⠀⢀⣠⠤⠔⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠙⠒⠂⠀⠀⠈⠓⠤⣄⡀⡀⠀⠀⣀⣀⣀⠠⠤⠄⠀⠀⡀⠈⠀⢀⡀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣸
⠀⠀⠀⠀⢆⣀⣀⣀⡤⠴⠊⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡽⠛⠋⠉⠁⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⠏
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠦⠀⠀⠀⣀⣀⠤⠀⠈⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⣀⠴⠃⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⡥⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣲⠖⠒⠊⠁⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢤⣀⡀⠀⠀⢀⠫⠤⠤⠤⢤⣀⣀⣀⣀⠠⠤⠤⠔⠒⠒⠛⠉⠁⠀⠀⠀⢰⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡈⠉⠑⠚⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣄⡀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⠤⣀⠤⠛⠲⢄⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢰⡀⠀⠀⠈⢧⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢧⠀⠀⠀⠈⠳⣤⠤⢤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠘⡄⠀⠀⠀⠀⠘⢆⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠄⠘⢶⠲⠿⢿⣦⣬⣆⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠉⠉⠓⠢⠽⣻⣅⠀⠀⠈⢧⠀⠳⡀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⢀⣤⢷⡀⠙⠿⢟⣉⡭⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠁⠒⠒⠛⠺⢦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡊⠳⠀⠀⠢⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⡍⠟⠐⠷⠓⠂⠀⠀⠀⠀⠀⠀⣶⢠⣆⣤⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⢡⡠⣶⡖⠈⡇⠀⠀⠀⠀⠀⠀⠀⣧⣼⠷⠄⡄⢿⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⣺⣬⡹⣦⣴⡆⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠙⠿⢷⣷⡌⢓⢻⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣻⡯⣭⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡉⡶⣿⡿⡇⠚⢻⣿⣿⢻⡟⣶⣶⣶⣿⡿⢿⣿⣿⣿⢿⢯⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢈⣷⣿⠁⢠⣰⢯⣿⡯⢉⠡⠀⢨⡃⠾⢛⣿⡚⢷⣾⣿⣲⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣝⡗⣾⣵⠶⢾⠟⢽⣟⣋⡜⢀⠠⣤⣀⡘⠬⣤⢴⡿⡷⣝⢼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠸⠟⣸⢩⡹⡇⣀⠐⣞⢮⠳⣻⠷⠈⠇⠁⣡⣸⠖⡿⣘⣯⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣻⣯⣌⠳⠮⢳⠚⢘⠮⠠⡂⡝⠢⣶⣙⣮⣻⣥⢿⣿⣟⠻⢿⣭⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣼⡇⣿⠆⢤⡃⡰⠾⠆⢦⡀⣧⣽⣿⣿⣿⣷⡾⠛⠁⠉⠌⢽⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣮⣅⠲⠂⢓⣹⢠⣬⣉⠹⡿⢿⠟⠛⠛⠉⠀⠀⡠⠘⠀⣠⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣃⠁⡦⠙⠛⡂⠆⠌⣁⡠⣴⡀⠴⠄⠀⢤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣅⣉⡰⣦⢦⠀⢈⠁⢬⠉⣾⣾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣼⣿⣤⡸⢁⣤⣤⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⡙⠀⠈⠻⢿⣷⣟⣉⣡⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠂⠙⠁⠀⠀⠀⠀⠉⢹⢿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⡠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣨⣉⡁⢁⣼⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⢿⢏⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⣶⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⢸⡏⣹⠅⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠙⠋⠛⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠃⡄
⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠈⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⣤⠴⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⢀⠌⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡅⣀⡇⠀⠀⠀⠀⠠⣴⠄⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠔⢁⡠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠑⠚⠀⠀⢀⠀⣰⠔⠊⠀⠀⠈⠒⠚⠺⠶⠵⠀⠀⢀⠀⠀⠀⠂⢁⠄⠋
⠀⠀⠀⠀⠀⠀⠓⠛⠄⠒⠤⠄⠓⠔⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⡀⠔⠉⠸⠀⠐⠊⢁⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠉⡤⠔⠊⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠡⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⡄⠔⠂⠄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠤⢀⣀⠀⠂⠀⣔⠒⠒⠛⠉⠒⣒⠆
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠭⠡⢉⡡⡌⠭⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠀⣀⡀⠀⠀⠀⢀⡀⠀⠀⠠⠀⡠⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣻⣯⡟⠋⠑⢠⣤⠄⠒⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠚⠭⢭⢿⠯⢑⣿⣿⡗⠺⢙⣴⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠒⠛⢋⠥⠖⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⣇⡤⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⣍⣝⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠺⠀⡀⠀⠀⠀⢹
⠀⠀⠀⠀⠰⢿⣒⣤⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣐⠀⠀⠀⠀⠀⠨⠼
⠀⠀⠀⠀⠀⡳⣟⠈⡀⠀⠑⣦⠤⢤⠐⠖⠒⡒⠲⡂⠸⠃⠀⠀⠀⠀⠀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠈⣧⣤⣀⡒⢈⠅⡀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢈⣙⡀
⠀⠀⠀⠀⠀⠀⠀⡠⢼⢇⠀⠀⠀⠀⠠⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⡴⢻⣤⣔⣀⠠⢀⢀⢀⢀⠈⠀⠈⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠞⢏⡆⢀⡴⢛⣠⣬⣾⣦⣤⣤⣶⠶⡆⠀⠀⠀⠀⠀⠈⠒⢦⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣟⢿⣞⠛⠃⠁⠠⠝⠴⠏⠃⠗⠀⠀⠀⠀⠀⠤⢁⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⠂⠀⠀⠀⠀⠐⠄⠀⠀⠁⠀⠀⠠⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⡆⠀⠀⣠⠄⡀⠄⠈⡀⠁⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠶⣄⠀⡀⠠⠀⡐⣱⣦⣖⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠿⠋⠙⠠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣷⣄⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⣿⣿⣷⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⢗⣀⡉⠙⣿⣿⣿⣿⡀
⠀⠀⠀⠀⢀⣀⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠉⠉⠩⣿⣿⠉⠛⣿⡁
⠀⣿⣟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⣠⠀⠀⣠⣼⣯⠬⠷
⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⡏⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠘⢻⣿⣷⣼⣿⣿⡅
⢸⡏⠙⣻⣿⣿⣿⣿⣛⠻⣿⣿⣷⣌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣟⣿
⠀⢙⣿⣿⣿⣿⣿⣿⣿⣷⣌⡛⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃
⠰⣯⣀⣻⣿⣿⣿⣿⡿⠟⠛⢛⡛⠿⢿⡝⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣧⡞⠀⠀⠀⠀⠀⠀⠀⣼⠀⠈⢿⣿⡿⠟⠃
⣠⣤⢿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠷⠄⠀⠘⣿⣆⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣴⣶⣶⠶⡶⠻⠟⢫⣿⣿⣧⣤⡔⠀⠀⠀⢀⣾⣿⡄⠀⠘⢿⡇
⠻⢤⣼⣿⣿⣿⣿⣟⣥⡶⠖⠂⠀⠀⠀⠘⢶⣾⣿⣿⣶⡿⣿⠟⣿⠟⠋⠘⠋⠁⠀⠀⠀⠀⠀⠀⠈⠋⣿⠋⢿⣧⣴⣀⣠⣾⠇⢸⣿⠀⠀⢘⡇
⢴⡞⢋⣡⢀⣾⣿⠋⠁⣀⣤⣤⣴⣶⠦⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠙⢿⡿⡿⠀⠈⣿⣧⢀⣀⡇
⠈⠻⢿⣴⣿⣿⣿⣿⠟⣛⣽⣿⠃⠀⠀⣠⡞⠀⠀⢀⡀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠘⠇⠀⠀⠀⢹⣿⣿⣿⠃
⡶⢶⣿⣿⣿⣿⣯⣵⣿⣿⣋⣤⠀⠀⣰⠏⠀⠀⢠⠏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠇
⠙⢦⣝⣿⣿⣿⣿⣿⣿⢿⣿⣷⣿⢇⡿⠀⠀⠀⡿⠀⠀⠀⢰⡏⠀⠀⢠⡖⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⢈⣭⣭⣽⣟⣫⣵⣾⣿⣿⢋⣾⣧⠀⣼⠁⣇⠀⠀⠀⢸⡇⠀⠀⣼⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠘⣯⣝⣻⣿⣿⣿⣿⣿⡏⣼⢻⢣⡖⡇⠀⣿⢖⣀⣾⣼⣇⢀⠀⢿⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⡇⣼⣸⣸⣧⣴⣿⣾⣿⣿⣿⣉⣉⡀⣸⠶⠂⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠻⢮⣽⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⡿⠟⢁⣹⣿⣿⠷⣿⣿⣿⣿⣿⡏⢀⣤⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢁⢀⣴⣾⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣼⢻⣿⣟⣿⣿⠿⢟⣿⣿⣯⣴⡾⣛⣋⣩⣤⣴⠾⣟⣿⠛⠛⠛⠛⠙⠷⣤⣤⣤⣴⣶⣾⣿⣿⣿⡿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⣷⢸⣷⡿⠛⢿⣄⠿⠿⢿⡿⠿⠿⡿⠛⠋⢁⠼⣿⣿⣿⣷⣿⣤⣤⢴⣺⣿⣤⣤⣴⣿⡿⢿⣿⣯⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢽⣺⣿⣷⣶⡊⢙⡋⠑⠄⠀⠀⠠⣿⣶⡿⠏⠈⠙⠛⠁⣸⣿⣿⢿⣿⣿⣿⣷⣿⣿⣣⣶⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣥⣄⣠⣀⠀⣀⣬⣿⡄⠀⠀⠀⠀⠴⠛⢉⡄⠈⢉⡼⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣆⡀⠀⣠⣤⣠⣶⠟⠀⢀⡄⠠⠾⢿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣶⣿⣯⢷⣭⠛⢿⠿⠛⠟⠋⢱⣆⣤⣼⣷⣷⣶⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣷⣷⣄⣤⣈⣿⣷⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠛⠛⠋⠉⠉⠛⠛⠻⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⡾⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠉⠉⠹⡇⢘⣳⣶⣮⣿⣷⣶⣤⠤⠄⢀⣠⣤⣤⣿⣬⣽⣿⣿⣿⠿⠷⣶⣶⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⣿⣯⣽⣍⡛⠳⠞⠋⠉⠉⠉⠀⠀⠈⠻⠿⠟⠳⠦⡤

⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⢦⡀
⠀⠀⠀⠀⠀⣀⠀⠁⠀⠀⠈⢉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂
⠀⠀⠀⠀⡎⠀⠁⠐⠚⠛⠯⡉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢠⡇
⠀⠀⠀⠀⡇⡔⠀⠀⣰⡄⠀⢸⡀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡼⢻
⠀⠀⠀⠀⠘⠲⠄⠀⠙⠁⠀⡘⠀⠀⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠊⠁⠀⠀⠀⠀⢸⡀
⠀⠀⢀⠀⠀⠀⠴⠀⠀⢆⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠈⠉⠉⠀⠀⠀⠐⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⡀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⡐⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⡀⠀⠀⠀⣧
⠀⠀⠀⠰⣄⣀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⠆⠀⠀⢹
⠀⠀⠀⠀⠈⠀⢒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠋⠀⢠⡏
⠀⠀⠀⠀⠀⠀⢃⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠢⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠈⠋⠶⡆⠀⠀⢀⡘⠀⠀⠀⠀⠀⠘⠢⣀⠀⡤⢀⣀⣀⣀⣀⡠⠤⠒⠉⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⡦⢤⠤⠤⠤⠤⠒⡞⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣄⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠂⠁⠀⢀⣉⣁⣆⠀⠟⠀⠈⠒⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠩⠐⢊⠃⠀⠁⢐⠶⣂⠤⠤⠀⠐⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠘⠊⠀⠀⡥

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣭⢉⡽⠷⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⢈⣆⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠘⠷⣽⠷⣾⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣤⢣⠈⣣⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠸⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⢢⡃⠰⠁⠀⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⣆⣢⠳⢠⠷⠲⠛⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠲⣌⢁⣀⣀⣠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢈⠛⡶⢀⣿⡴⠩⢅⣚⢃⣤⢀⠀⠀⠀⠀⢀⡀⠛⡟⢒⠭⢭⡠⢍⡑⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣐⠶⠼⣁⡽⠠⣴⣏⠩⢭⣶⣚⠿⣠⠜⣹⡊⢿⣂⡛⣺⢱⡜⡿⠤⢪⣄⡭⢸⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⣾⣩⠸⠤⡃⠴⠿⠶⣣⢀⢯⣙⣠⣎⣷⠀⢸⣯⣌⣭⠄⠷⣤⣁⣨⣄⣢⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣤⡌⠷⡸⢤⡶⢞⣪⣈⣇⡚⢃⠰⢿⣃⢾⡯⠜⣫⠙⢷⠶⡄⢘⣅⣤⣥⠛⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣿⡷⢀⣤⡛⣆⢤⣱⣉⢛⠞⠯⣖⣹⡞⠂⣉⡹⠛⡴⣡⢃⢛⢝⠛⢻⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡷⡿⢾⣣⣍⡞⣫⢭⣯⣿⠶⢮⡴⠻⣋⣽⢸⡊⣷⠀⠻⢏⡘⣻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢿⣋⡭⠛⠻⠿⡟⠏⣭⣈⣩⣅⣭⣉⣭⣿⣶⣩⣿⣧⠽⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣗⣻⠶⣺⣷⢘⣯⣽⣓⣒⣛⣻⣿⣿⣿⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣯⣿⣾⣥⣾⢴⡛⣽⣿⣿⣿⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣜⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠟⣿⣾⣶⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠴⢤⣀⡀
⠀⠀⠀⢀⡖⢊⣭⠽⠧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡏⠀⢴⠀⣿⢹⡦⣄
⠀⠀⠀⢸⡔⠁⡦⠰⡄⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⠀⠈⠀⢁⡏⠀⡼⢲⡄
⠀⠀⠠⠯⡼⠡⡀⠸⠇⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡥⠤⠀⠀⠀⣀⠾⠀⠈⠀⢊⡹⡄
⠀⠀⠀⠀⠣⣀⣽⠀⠀⠀⠀⠀⠀⢲⣤⣌⡳⣄⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁⠀⠀⠀⠀⠀⠘⢆⠀⢀⡶⠟⠀⠷⡄
⠀⠀⠀⠀⠀⠀⡟⠀⢀⠀⡀⢀⠀⢠⠀⠉⠛⠈⢦⣀⣀⣀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⣤⠖⣰⠁
⠀⠀⠀⠀⠀⢰⠇⠀⠚⡆⠧⠚⠂⠀⣀⡠⠀⠀⠉⠉⣀⠀⠘⠣⠤⣄⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⣨⠇
⠀⠀⠀⠀⠀⢸⠀⠀⣦⠇⠰⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⠤⣄⠊⠄⠀⢠⠆⠀⠀⠀⠛
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⢀⠀⢠⠃
⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⡀⠀⠀⠀⠀⠀⣴⠂⠀⡜⠀⢀⣉⡉⢩⡽⠂⠀⢁⠆⢀⠞
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢧⡀⠀⢀⠞⡅⠀⠔⢁⣠⠥⠖⠒⠉⠐⢶⣄⣠⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢠⣈⣀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠠⠠⠔⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉⠁⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⣀⣂⣀⡀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣛⣩⠽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣀⣀⢀⠀⣀⡴⣯⣭⠝⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⡹⠋⠁⠀⠀⢾⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡼⠀⠀⠀⠀⠀⠸⣱⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣄⣤⠴⠃⣃⣀⠀⢠⡶⣒⣚⡿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⠖⠒⠀⠉⠁⠈⠉⠀⠀⠋

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣰⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀⠀⢐⣹⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⢏⣉⡝⠞⣶⣿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠮⠠⠄⠨⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣀⣉⠻⠤⣦⣅⡬⣿⣧⡈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⠸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⣿⠘⠿⠄⣰⡟⢸⠏⠙⢿⡄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠄⠠⠀⠈⠣⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢆⣀⣠⣝⣻⠌⠠⡀⠼⠞⡄⠃⠀⠀⠀⠀⠀⠀⠀⡔⠂⠄⠀⠀⠀⠀⠀⠀⠈⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠈⢉⡛⢁⣀⡈⠡⠀⠨⡅⠀⠆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⡄⢀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠠⠄⠊⢁⠠⢌⣸⠀⢀⠖⡆⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠇⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡐⣙⡳⢧⣤⡃⢈⠀⣬⠀⠀⠀⠿⡤⠰⠀⠴⡄⠈⠂⠀⠄⠀⢰⣄⡠⡀⠈⣁⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠥⠴⢉⣧⠛⣁⣰⠒⠲⠂⠘⢠⠖⠙⡎⠡⡄⠃⠀⠀⠰⠄⢀⠙⠛⠛⠾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⡂⢄⠬⣀⢸⡄⠐⢻⡅⠀⡼⡁⠘⢁⢌⡰⠃⠄⡈⡰⠀⠀⢂⠀⠀⡈⠰⠀⠻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⡁⠀⠀⢘⠒⠒⠙⣻⠤⢊⡀⢿⠴⢃⠈⠁⢨⠞⣰⠇⠖⠀⢈⢀⣠⢠⣀⡎⣶⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡛⣟⣋⡽⠟⣂⣼⢀⡀⣠⢏⠀⢰⠉⢄⠁⠵⠶⢷⣤⠌⠈⠨⣷⣞⣍⣴⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠈⢻⣥⡶⠿⢷⠔⡋⠉⠁⠘⠀⠀⣄⠀⠄⠀⢰⠿⣿⣿⣶⢰⣿⢟⣿⢸⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡐⢀⡘⣽⠞⠲⠖⢛⣳⠇⡱⢀⠔⠀⠏⠀⠠⠀⠀⠀⢤⡘⣿⡿⢿⠇⡎⣻⡛⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣃⡌⢰⢿⡿⠖⠙⠉⠏⠛⢖⠀⠀⠠⠂⠀⠀⠀⢠⠘⡈⣥⣯⢥⢿⠀⣼⣿⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣭⡹⣒⣚⣪⠏⡲⠞⡁⠈⢀⡀⠔⠀⠁⠀⣥⠨⢦⠂⡗⣛⣼⢬⢾⢏⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣾⣿⣉⣠⠤⢴⣂⠁⠀⠀⠀⢀⡀⡙⣀⢂⠸⣀⠴⢙⡴⣣⣵⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣶⣶⣤⣾⣦⣀⣸⣮⣍⣥⣚⣤⣴⢉⣴⢾⠾⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠹⣿⣿⡟⡝⠋⢉⣴⣳⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡟⠀⠈⠛⠻⢿⣯⠷⠈
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢸⣷⣤⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⢀⣨⡄⣰⡿⢿⠉⢤⢀⣾⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠤⠈⠘⠉⠝⣀⠛⣘⣈⡥⠊⠈⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠫⣄⠀⣨⡀⢑⣋⣭⣥⣶⡀⣰⠟⠋⠀⠀⠀⠀⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠙⠉⠉⠐⠄⠚⢠⠋⠀⠈⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠈⠹⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⡲⢆⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⣤⠀⢀⣠⠄⢢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⠏⣉⡀⠀⣇⢱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢞⣀⣿⣾⣤⢸⡇
⠀⠀⠀⡀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡟⠈⠡⢻⣥⡉⠰⣱
⠀⠐⠉⡁⠤⠀⠀⢀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠈⠉⠳⢲⢀⡙⠃⠙
⠀⠀⠸⠃⢀⡚⠂⡐⠒⢌⠘⠂⠁⠤⢈⠀⠶⢢⡴⣤⡶⠀⠀⠀⠀⠀⠁⢈⠀⢈⠀⢱⢒⠀⣲⠄
⠀⠀⠀⠀⠠⣄⠀⢘⢂⢂⠉⠄⡂⣠⣤⠞⣈⠓⠐⠊⠆⠈⠒⢰⠁⡅⢢⠈⠀⠀⠁⠀⠄⣤⠟⡄
⠀⠀⠀⠀⠐⠇⡀⠐⡞⢃⣴⢔⡏⡨⢴⣃⣞⢒⣀⠚⣐⡈⢉⡡⠆⠲⠊⢄⠀⠂⠡⠔⢀⠜⢈⡀
⠀⠀⠀⠀⠀⠀⠙⠿⠛⠑⣦⣸⣧⣿⠛⣣⢞⡿⠀⢾⠠⠅⠀⠀⠀⠀⠀⠀⠤⠆⢀⣴⠉⡴⢌⡀
⠀⠀⠀⠀⠀⠀⠉⠀⠉⠄⠘⣉⡼⣥⢾⣱⡟⢂⣈⣌⠐⡢⢴⣠⡔⠈⡠⢇⠤⠢⠄⠘⠡⣱⢌
⠀⠀⠀⠀⠀⠀⠘⠀⣠⣷⡒⠋⠀⠞⠘⠻⢿⣿⣟⣉⡙⣦⣤⠽⠿⢟⡉⠀⠃⠓⡰⢦⣗⢉
⠀⠀⠀⠀⠀⠀⠁⡀⠈⠛⡥⠀⣘⡀⣠⣄⡀⢄⣀⠀⣈⣁⡀⢠⠇⡀⣁⢨⡘⢁⣧⣄⣸⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠂⠐⠆⠁⠈⠁⠀⠁⠀⠁⠉⠀⠉⠈⠡⣿⣿⣿⢻⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠈⠡⢴⡗⠀⠐⠐⢂⡒⢒⣹⣾⣲⣾⠿⠞⠋⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠩⠟⠩⣼⢟⠗⣧⠸⣿⡍⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢪⢽⠒⠈⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣠⣴⣾⣯⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⢿⡵⠂⠀⡿⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⣤⡁⠼⣿⠖⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⠀⣰⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⢯⣛⣾⣿⣾⣿⣽⡁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣡⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠇⠀⠈⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡟⣛⠛⠛⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠇⠀⠀⠀⠀⢠⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⢾⣿⣿⡟⠳⣾⣠⣴⡿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⢂⡀⠀⠀⠀⣹⣿⣿⣿⣿⢿⣿⢟⣓⠶⣶⣾⣿⣿⣿⣿⣿⣷⠿⢭⣀⣹⣧⣀⣚⣋⣽⠟⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣜⠀⠀⢀⣶⣿⣿⣿⠛⠲⣾⣭⡭⢿⠖⠿⢿⣯⣨⡿⡿⠿⣿⣷⣤⣌⣩⡿⠍⠉⣹⣿⡛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠀⢠⣾⣿⣿⡟⠛⠿⣿⡿⠶⢾⡛⢙⣿⠟⣁⣈⠉⠀⢀⣈⠛⠙⢿⣦⣍⠛⢻⡿⠁⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣄⠰⣿⣿⡿⠏⠙⠻⡿⠻⠶⣦⡶⢛⣿⠓⡾⢉⣥⣴⢶⠶⢶⡶⣶⣾⣿⣿⣿⠋⢛⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⢰⣿⣏⣑⣀⣉⣹⣟⣳⣾⣋⣿⣫⣴⣾⣿⣿⣿⠻⢧⣄⡰⠀⠠⣮⠋⠙⠛⣿⣿⣿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣇⣿⢟⠟⠿⠻⣿⣿⣿⣍⣻⣴⣚⣷⣿⣷⡉⠉⠳⣤⣀⣸⡷⠒⠒⢏⣀⣉⠀⠙⠃⠉⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⡀⠀⠀⠀⠀⠀⠉⠛⠋⣹⡿⢿⣿⢧⠉⠁⠀⠈⠁⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⡼⠓⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⡁⢠⡄⢀⠐⢀⡀⢀⣀⣀⣤⣀⠀⡀⠀⠀⠀⠄⢁⠤⢀⠀⣾⣧⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣤⣎⡳⢰⣟⡛⠽⠓⠯⣿⢿⣿⣷⠆⠀⠀⢾⣅⠈⠁⠙⠧⣜⣿⣿⣍⡧⢀⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⣿⣿⣿⣿⣷⣾⣤⣬⣿⣿⣧⡀⠀⠸⣿⡌⣷⡀⡀⠉⢻⣿⣿⣞⠀⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣧⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣧⡀⢠⡸⣿⣿⣏⡁⠀⠙⣿⡿⠿⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠉⠛⠻⢧⣿⣶⣬⠛⠷⢴⠣⣶⣮⠭⢷⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⡀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⣤⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡰⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢰⣿⠛⠳⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠙⠎⢀⣠⣋⣽⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠔⢢⣿⢦⣩⣿⣱⣿⣿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠄⣠⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣶⣿⣿⡟⠛⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⢿⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⡏⠁⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣧⣵⠂⣸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠕⠀⠀⠀⠀⢦⣿⣿⣿⣶⣦⡤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣽⣗⡛⢻⣧⠀⠽⠟⣻⡖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡰⠀⠀⢠⣤⣿⣿⡿⠯⣬⣟⣒⣿⡥⣿⣿⣎⢙⢿⣿⣿⣷⣌⣙⠛⣿⡋⠛⢫⣷⠞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⢀⣼⣿⣿⠟⠳⣶⣿⡯⣶⠞⠓⣶⠟⠉⡙⠃⠀⣈⡻⠝⢿⣭⡝⠒⢲⡿⠉⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣆⢠⣿⣿⠿⡙⠛⣷⠿⠷⣤⣴⠛⣿⠇⡾⢉⣡⣤⣤⠬⣴⣶⣾⣿⣿⣗⠋⢓⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⢸⣿⣏⣢⣈⣉⣿⣛⣶⣟⡿⣫⣕⣾⣟⣿⣟⠻⣦⣄⠆⠀⢿⡛⡙⠛⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⡿⢛⠟⠟⢻⠿⣿⣯⣹⣷⣪⣷⣿⣷⣉⡈⠳⣄⣠⠾⠖⠒⠊⣁⡉⠀⠈⠃⠁⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠋⢩⠟⢻⠿⠶⠉⠀⠀⠀⠀⠂⠦⣀⠀⠀⠀⠀⠀⠀⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⣠⠀⢀⣀⣤⣂⠤⣄⣶⣤⡄⠀⠀⠀⢀⠀⢦⢀⣄⢸⣷⣶⣦⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣤⣌⣾⣼⣝⣏⣑⡻⠻⣿⣿⡇⠀⠀⢻⡆⢀⡀⠙⢦⣽⣿⣧⣟⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣯⢙⣿⣿⣿⣿⣿⣷⣶⣿⣿⣷⡄⠀⠘⣿⣼⣧⠤⠀⢨⣿⣿⣿⣠⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⡿⠿⢿⣿⣿⢿⣝⠻⣿⡄⢓⠜⣻⠿⣦⣀⣠⡞⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⠃⠀⠉⠙⠘⠋⠋⠈⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣜⣹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡖⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⢋⡜⠁⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡒⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢼⣿⣤⣾⡅⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣦⣶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⢛⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⢿⡛⣿⣿⣿⣤⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠨⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣟⣦⡼⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣿⡏⣳⣿⣿⣾⣬⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣇⠹⠻
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣮⣝⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⣿⣻⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣀⣤⣿⣟⣿⢟⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠿⠞⣿⡄
⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢷⣦⣶⡹⣧
⠀⠀⠀⠀⢲⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⢿⣏⣻⣯⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⡏⠻⠆⢹⡄
⠀⠀⠀⠀⠘⢿⡿⠻⢿⣿⣿⣿⣿⡿⢷⣾⣿⣿⢿⣟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣱⣬⡀⠀⠀⠙⢂
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⢷⣾⣿⣯⣿⣾⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣻⣽⠟⡿⢿⣷⣿⠟⠃⢀⠐⠀⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠷⣾⣿⣿⣿⣿⣿⣾⣿⡇⢀⣀⣀⣤⠂⣠⡆⣰⡿⠻⣿⠿⠾⠿⢷⣦⣿⣤⣤⡼⣄⠐⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣿⣿⣿⣿⣯⢿⣧⣽⣿⣿⠛⣽⢟⣼⡿⣶⣿⣦⣾⠟⠁⠀⠄⠀⢀⠙⢿⣿⡿⣿⠀⠟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣶⣿⣿⣿⣯⡙⣷⣿⣿⣿⣿⣾⣇⣿⣿⣤⣯⣄⠉⠀⠀⠀⠀⠀⡀⠈⡁⠀⢿⡟⠀⣀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣇⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⢀⠀⠀⠀⠰⠀⠋⠰⠇⠀⣸⡷⠈⠿⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣶⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠆⡴⠀⠋⡀⠸⠃⡄⢰⡇⢀⠀⣰⣟⡼⠟⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣏⠙⣠⠀⣾⠇⢠⡀⠃⠀⠀⣨⣾⡟⢻⣷⠿⣷⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣇⣈⣀⣿⣧⣴⡾⣿⣿⣯⣾⣛⣿⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠿⣿⡆⠀⠩⣙⣟⢿⣾⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣟⣿⣿⣿⣽⣆⣾⠟⢂⣴⣿⣿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣧⣼⢋⣴⣿⣷⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡇⢠⠈⠻⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠀⠈⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⢀⠀⢀⣀⢠⣶⣤⣤⣤⣤⡥⠘⠷⠊⠓⣄⡠⣤⣤⣀⣶⣄⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠈⠑⠋⠑⠖⢠⣬⡿⢻⣷⣤⢠⣌⣙⠛⠛⢿⣶⣭⣿⣿⣿⢿⣷⡟⠉⠣⠦⠘⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠐⠒⠛⢿⣦⠟⢿⡿⠻⠿⣛⡛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣾⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠠⡾⢂⣏⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠓⠿⠷⠮⢤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠐⠐⢆⠒⠀⠀⠐⢉⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠐⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⠖⠋⣏⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢀⠎⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡄⢠⡏⠀⠀⠀⠀⠀⠐⡞⠂⠄⢀⠀⠀⠠⡀⢀⠀⠀⠀⡀⠀⠀⠀⠊⡠⠈⢁⡤⠢
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠈⠁⠀⠀⢀⣀⣀⡗⠊⠁⠀⠀⠀⠉⠋⠚⠃⠒⠂⠀⠈⢀⡀⠀⠀⠉⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠑⠂⠑⠤⠔⠙⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⢀⢀⠤⠰⠀⢀⠠⠂⠁⡘⠀⠐⠋⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠁⠀⠀⠀⠉⡤⠔⠊⠁⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠈⠄⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⠤⠒⡀
⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠨⠤⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠑⠢⣀⡈⠀⠀⠀⠄⠀⣀⢀⣠⠔⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⡀⠠⠀⠀⠉⠙⠒⢒⠒⢒⠒⠒⠀⠂⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡐⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⡀⢠⣄⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⡤⡤⠤⠤⡴⠄⠀⠀⠀⢀⡠⠋
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡮⢽⢻⣍⣅⡈⢰⢲⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⠒⣛⡟⡒⢹⠿⢿⡏⠙⣈⣶⣰⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠭⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣷⣼⣧⣿⣧⣾⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⢤⣤⣀⠀⣅⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⡀⠀⣀⠀⠙⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠼⠋⠀⢀⣀⣀⠉⠽⢿⣮⢶⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⢨⠛⠀⠉⣠⣶⡤⠘⠂
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠿⢻⣿⣷⣦⡙⣷⢳⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠈⠳⠤⣼⣿⠏⣧
⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⠤⠴⠟⠒⠲⣿⣿⣮⢿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠕⡁⠀⠀⠀⠀⠀⠀⠸⢟⣠⠃
⠀⠀⠀⠀⠀⠀⣿⣡⡎⢁⣠⡶⠆⠀⠀⠀⠉⠛⠃⢹⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠙⡀
⠀⠀⠀⠀⠀⢠⣯⣤⡴⠛⢱⣛⣯⣽⢿⣽⡦⡀⡄⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡿⢫⠇⢀⢀⢀⠁⠀⠀⠀⠀⠠⡀⠀⢃
⠀⠀⠀⠀⢀⣿⣿⠿⣡⣦⣿⣿⣛⣟⣿⣷⣝⣦⣰⣦⢼⣄⣀⣀⣀⣀⣠⠤⠀⠘⠀⡁⠀⣳⠀⡈⣼⠘⢀⠀⢢⠀⠀⠁⠄⢸⡀
⠀⠀⠀⠀⢸⣿⡟⢠⣿⣿⣿⡵⠛⠋⠉⢀⣠⢯⣴⠾⠿⠶⠾⣿⣿⣁⣟⡗⠾⠀⡠⢫⡇⠿⠈⡁⠈⡄⠘⣇⠠⠣⠡⠀⠌⠠⡇
⠀⠀⠀⠀⢸⣿⡇⣾⣿⡿⠑⢋⣴⣿⢗⠔⣾⡿⢁⣠⣤⠀⠐⣾⠏⢁⠈⠷⠲⠚⠴⢿⡶⠃⡰⡇⣼⢃⠀⠸⡇⠇⠄⠀⡀⢰⠃
⠀⠀⠀⠀⠈⢿⣧⢿⣿⡇⢀⣿⢱⡏⡾⠃⣻⢃⡾⠋⠀⣠⣿⠏⢌⣲⣆⠐⠌⣻⡄⡰⣄⣠⠄⢐⣩⣬⢠⠆⡦⠰⠠⠁⢂⡞
⠀⠀⠀⠀⠀⠈⠻⡌⢿⠃⢸⣧⣿⣷⣧⣞⣿⡟⣠⠀⣾⢫⡳⣌⡀⢒⠆⡛⢛⣭⡬⠡⠶⢖⡶⣪⣝⣧⠏⣴⠃⠍⠄⢄⠞
⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⢸⣿⣿⣿⡿⣸⣿⡴⢁⡼⠁⣨⣽⠀⠥⡈⠳⠶⠖⣲⣭⠜⢣⣬⣥⡿⣉⣥⡾⢋⣁⠸⡷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡏⣿⣿⣿⡇⣿⣿⣣⣾⣷⣿⡿⠿⢓⣶⣦⣝⣻⣴⣶⣶⣿⣶⣶⡶⣿⣿⣿⡿⡞⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠣⣿⣿⣿⡇⣿⣿⣿⣿⡿⠃⠀⢀⠀⢒⢀⡉⠉⡰⡝⣻⢿⣟⣿⣿⣿⣿⣿⣆⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠻⡝⢩⣿⣿⣿⣿⣧⣶⣦⢈⡀⠲⢤⢠⣴⣇⣿⣟⣿⣿⣿⢿⣻⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡛⠁⠘⣿⡹⠃⠙⢷⣶⣰⢴⣦⣤⣶⣾⣿⣿⡟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠛⢥⡭⠟⠝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢂⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢧⣀⠿⣶⡤⠴⣴⣦⡤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡮⠼⢮⣓⠦⠬⣥⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠛⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠀⠐⠀⠀⠀⠤⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢠⡰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡈⢿⠧⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⢀⠠⠐⠂⠉⣀⣀⣀⣀⡀⢁⠶⠭⣓⠦⡀⠀⠙⠔⢅⠁⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡠⠖⠀⠠⠖⠛⠉⢉⡔⠣⢌⢙⠣⣍⡒⢌⠳⡄⣄⠀⠀⡀⡀⡢⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠌⠀⠴⠐⠁⠀⠀⠀⠀⠀⠑⠰⢯⡈⠑⠠⣁⠡⡄⢉⠀⢣⠙⣌⠳⣄⠀⠘⠄⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠑⠈⠢⠑⡇⠘⡄⠠⡀⠑⢬⣑⠲⣄⠀⠂⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⡀⠀⠘⡀⠡⡘⢤⡘⠂⡀⡀⠂⢤⡑⣌⢣⠁⡀⠈⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⢀⠂⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠒⠄⡁⠑⣄⠳⡜⢆⠱⢌⠢⢤⡂⠈⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠔⠀⠀⢀⠀⠀⠀⠀⠀⠀⠢⡙⢅⠈⢢⠙⠀⡑⠦⡽⠊⠀⢦⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠄⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠣⡀⢡⠈⠢⢌⡀⠀⠀⠀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⡐⠀⠌⠀⠀⠀⠈⠃⠠⡄⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⢆⡈⠑⢢⠍⠀⠀⠀⠀⠐⠀⠑⡀
⠀⠀⠀⠀⠀⠌⠀⠘⠄⠀⠀⠀⠀⠠⠀⢳⡀⢀⠀⠤⢤⠤⠂⠀⠲⠂⠰⠂⠐⠢⠄⢀⣀⠀⠀⠀⢠⠏⠢⠌⠛⠀⠀⠀⡀⠀⠀⠀⠀⠄⠈⠄
⠀⠀⠀⠀⠌⠀⡐⠀⠘⡀⠀⠀⠀⠀⡡⠤⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠰⣏⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠈⢂⠈⠂
⠀⠀⠀⠐⠀⡐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠈⢄⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⣶⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⢸⡏⣹⠅⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠙⠋⠓⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠃⠄
⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠈⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⡤⠴⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⢀⠌⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡅⢀⡇⠀⠀⠀⠀⠠⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠔⢁⡠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠑⠊⠀⠀⢀⠀⣰⠔⠊⠀⠀⠈⠒⠚⠺⠶⠵⠀⠀⢀⠀⠀⠀⠂⢁⠄⠋
⠀⠀⠀⠀⠀⠀⠓⠛⠄⠒⠄⠄⠓⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⡀⠔⠉⠸⠀⠐⠊⢁⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁⠀⠀⠀⠉⡤⠔⠊⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠡⡀⠀⠀⠐⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⢬⡄⠔⠂⠄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⢄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⠤⢀⡀⠀⠂⠀⣄⠐⠒⠛⢩⢶⣖⠆
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠭⠠⢉⡡⡨⠩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠀⣀⡀⠀⠀⠀⢀⡀⠀⠀⠠⠀⡠⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣻⣯⡟⠋⠑⢠⣤⠄⠒⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠞⠭⢭⢿⠯⢑⡿⣿⡗⠺⢙⣔⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠒⠛⢋⠥⠖⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⡠⠀⡀⠀⢀⠢⢤⡀⠀⠀⡏⠀⢻⢀⡤⣠⠊⠉⠀⣀⠤⠄⠀⢞⢡⠀⠑⢆⠀⠐⠤⡀⠀⠀⡞⢳⡄⠀⢠⠟⠓⠦⣔⠒⠓⠦⣄⣀
⠀⠀⢀⠰⢀⠑⣄⢻⠀⡠⠓⠀⠀⠈⠓⠁⠸⡀⣀⠇⠀⢸⣇⠀⠀⠀⠈⠉⠁⠉⠁⠤⠤⠒⠳⡄⠀⣧⣸⠃⢀⡟⠀⠀⠀⠈⠙⠒⠶⢤⡈⠉⠉⢱⡀
⠀⠀⠀⠂⢢⣽⣿⡻⠋⡠⠔⠒⠉⠉⠓⠦⣀⠀⠀⠀⠀⢸⣧⠤⢄⣀⡀⠀⠀⠀⠈⢉⣀⡈⢽⡃⠀⠼⠁⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⢀⡟⡄
⠀⠀⠀⢊⢀⠔⠁⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⢸⡅⢀⡀⠀⠈⣈⡉⢉⣉⣀⠀⠀⣰⠇⠀⠀⣠⠞⠀⠀⠀⠀⠁⠀⠀⣠⢎⡵⠁⠀⡼⡸
⠀⠀⠀⠀⠁⢀⡎⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠈⣇⠀⠙⠒⠦⠬⠤⠤⠄⠀⢀⣀⠠⠤⠘⠁⠀⠀⣧⣀⠀⠀⠐⠀⠀⠀⣰⢣⠏⠀⠀⢠⢇⡇
⠀⠀⠀⠀⠀⠸⣇⠠⡀⠀⠀⢀⡞⠁⠀⠀⠙⢦⠀⠀⡿⠀⡴⠾⠶⡆⠀⠀⠀⠀⠀⠠⢤⣄⣀⠀⠀⠀⠘⠫⢽⣲⡦⣄⠀⢠⠇⣾⣀⣀⣠⡼⢸⠁
⠀⠀⢀⣤⣄⠀⠙⢦⡀⠀⠀⠘⣇⠀⡀⢀⡄⣸⠀⢠⠇⢸⠁⠀⣰⠏⠀⢠⠒⠒⢦⡀⠀⠀⠈⣧⣀⣀⣀⣀⣀⡈⠙⠲⣝⣫⠞⠓⠶⠶⠶⠖⠋
⠀⠀⣾⠁⠈⠳⣄⠀⠉⢦⡀⠀⠈⠳⠬⠵⠞⠁⢠⠟⠀⠘⠒⠚⠁⠀⠀⠘⢮⣀⣠⡇⠀⢰⣯⣽⣏⣀⣠⣤⠤⠽⠇⠀⠀⠀⠀⠀⢠⠖⠒⠲⡄
⠀⠀⣿⡄⠀⠀⠈⠑⢤⣀⠑⢄⡀⠀⠀⢀⣠⡴⢋⣠⠴⠖⠒⢛⡓⠒⠲⢦⡀⠀⠀⠁⠀⢸⠀⠀⢹⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠏⠀⠀⠠⢹⡀
⠀⠀⠸⣷⡀⠀⢀⣤⣤⡈⠑⢦⡈⠉⠉⠉⠁⡴⢯⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠲⢄⡀⠀⠸⣄⠤⠤⢷⡤⠤⠤⣤⡇⠀⠀⠀⢠⣾⠀⠀⠀⠀⠃⢦⡀
⠀⠀⠀⡟⣧⠀⢻⠀⠀⡝⣦⠀⢹⡄⠀⠀⡞⠀⠈⣧⠈⠀⠀⠀⠀⠀⠀⡎⠀⠀⢠⢙⡆⠀⣟⠒⠒⠚⣷⠚⠛⢉⡇⠀⠀⠀⠸⡍⢙⠋⠙⠉⠉⣩⠁
⠀⠀⠀⢿⠘⣇⠀⠳⢤⣤⠟⠀⢰⠇⠀⢰⠳⣕⠀⠘⣆⢀⣒⣒⣀⣀⣸⣇⣀⠐⣡⠞⢳⠀⢻⠀⠀⠀⠸⣆⠀⢸⠃⠀⣀⡀⠀⠙⠾⣷⣤⡤⠞⠁
⠀⠀⠀⠈⢧⣈⠳⢤⣀⣀⣠⣴⠟⠀⠀⢿⣐⣨⠷⠞⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⢧⣀⣸⠇⠈⢧⣀⣀⣀⣉⣠⠜⠀⢯⠉⢧⠀⢀⣠⡴⠀⠢⣄⡀
⠀⠀⠀⠀⠀⠉⠛⠒⠒⠛⠋⣁⣀⣀⡀⠀⢉⣁⡀⠀⠀⠀⠸⡳⣶⣄⡇⠀⠀⠀⠀⠈⠁⢀⣴⣦⣍⡉⠉⠀⠀⠀⠀⠈⠓⠻⣄⣈⡓⠶⠴⠶⠞⠃
⠀⠀⠀⢰⡒⠦⣴⡒⠋⢉⣉⣀⠠⠀⠉⢶⡁⠀⡝⠀⠀⠀⣠⠽⠾⢿⣧⣠⠤⠤⣄⡀⠀⢸⣝⡻⠷⣯⣭⣍⣉⣉⣉⣛⠲⢤⣀⠈⠉⠓⠦⣄
⠀⠀⠀⠘⣧⠀⠱⢭⣒⣤⣀⠀⠠⠄⠀⠀⠱⡀⢨⠆⠀⣼⢡⠊⠈⠀⠈⠁⠀⠀⢠⠹⡄⠈⠻⢿⣷⣶⣶⣯⣭⣭⣽⣛⡻⠶⣌⢳⡄⠀⠀⠘⣆
⠀⠀⠀⢰⡿⡦⢤⡘⣿⣭⢻⢷⣦⣄⡀⠀⠀⠑⣌⠆⠀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠶⠤⢤⣉⣉⣉⣉⡉⠛⠻⢷⣼⠋⠀⠀⠀⠀⣿
⠀⠀⢀⣀⠓⢬⣒⢵⡀⠛⠉⣟⠀⠛⢿⢗⠦⣄⡈⣧⠀⠸⡆⠀⠀⠀⠏⠘⠆⠀⠀⢰⠁⠀⢸⠭⠶⠶⠶⠶⠶⠦⣭⣍⡓⠤⡉⠀⠀⢰⠋⠉⠉⣹⠂
⠀⠀⠀⠈⣳⡀⠈⠑⠮⣓⢦⣈⠉⠳⡀⢀⡙⠲⠽⠇⠀⠀⠹⣔⠤⡀⠀⠀⠀⠄⣠⠏⠀⠀⠘⠿⢿⣒⣒⣒⣒⣒⠢⠌⡙⣾⠀⠀⢠⡟⡶⠒⢲⣿
⠀⠀⠀⠑⢿⣧⣤⡠⠴⡌⠑⢬⡓⢦⣉⣁⡸⠂⠁⢀⣀⠀⠀⠈⠓⠒⠛⠓⠒⠛⠁⠀⣀⣤⠴⠶⠲⠶⠦⣄⡀⠈⠙⢦⣄⣷⠀⠀⠸⠶⢷⣬⣿⣸
⠀⠀⣠⢾⡿⠋⠛⠒⠋⠀⠀⠀⠈⠓⠖⠋⢀⡠⠞⠉⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⢉⢳⡀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠈⠁
⠀⠀⠉⢁⡤⠤⠤⠄⢤⣄⣤⠤⠤⡀⠀⠀⡿⠤⠤⠤⠤⢤⡴⢦⣄⣈⣓⠲⢄⠀⢸⢿⠀⠀⠀⠀⠀⠀⠀⠀⡰⡠⠃⢀⡴⠞⣻⠋⠉⠉⠉⠓⢦
⠀⠀⡎⢹⠉⣿⠛⠛⠛⠛⠛⠛⠛⡏⠀⠀⣛⣷⠀⠀⣀⠀⠙⠋⠀⠀⠉⠉⢻⠀⠈⢧⡳⢤⡀⠀⠀⠀⠀⠀⢸⠁⢀⡞⠀⢎⠉⣠⠶⢶⣄⠀⠈⢧
⠀⠀⠹⣼⣧⠘⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⣯⡀⠀⠸⠽⠂⠀⣠⣤⣄⠀⠀⢳⠀⠀⠀⠙⣆⢷⠀⠀⠀⠀⠀⠘⡇⠸⡇⣠⠊⠘⣇⠀⣸⣽⠀⠀⣸
⠀⠀⠀⢠⡛⣦⣀⡀⠀⠀⠀⣠⠗⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⠛⠶⠟⠀⠀⢸⠀⠀⠀⠀⢿⢸⡆⠀⠀⠀⠀⠀⢹⠀⢷⡸⢄⣠⣌⢉⣩⣁⡖⣲⠏
⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠙⠒⠒⠒⠒⠒⠚⠙⠒⠒⠒⠒⠚⠀⠀⠀⠀⠈⠳⣧⣄⣀⣠⣤⡤⠞⠀⠀⠙⠶⣤⣈⣉⣠⡭⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢠⣠⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⣯⡇
⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠃⠀⠀⠀⠀⢀⣴⠶⠂⢙⢻⣶⣤⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠉⠙⠠⠴⠂⠀⠀⠀⠀⠀⠀⠐⠉⠀⠋⠈⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠉⢛⠋⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡇⠀⠀⠀⠀⠀⠠⢆⡀⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⣷⠼⠃⠀⠀⠀⠀⣰⣶⡀⠀⠀⠀⣴⣾⣶⣿⡆
⠀⠀⠀⠀⠀⠚⠻⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠠⢬⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣜⡉⠜⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣠⣷⠀⠀⠀⠀⢰⣟⡀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢈⣿⣧⣀⣀⣀⣠⣿⠏
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢘⣉⡵⠤⢤⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠉⢾⣿⣿⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡿⠏
⠀⠀⠀⠀⠀⠁⣀⡊⠉⣇⣀⠀⠀⠀⠀⠀⠀⢀⣈⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡾
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠉
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒
⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢀⣤⣤⠠⣄⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡌⠀⠀⠀⠂⣴⣿⣟⣿⣷⠈⠉⠀⠲⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄
⠀⠀⠀⠀⣸⣷⠂⠀⠀⠲⠿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠅
⠀⣀⠤⠚⢿⠾⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶
⣾⣁⣤⣤⡶⠶⢶⡿⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿
⠀⠉⠳⠠⢤⣤⣬⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠺⠦⠂⠀⠂
⠀⠀⠀⠀⠀⠈⠙⠻⣷⡀⢸⡷⢦⣤⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⣀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣦⡰⣬⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠻⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠿⢷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣀⣀⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣰⣦⡦⣀⣴⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠿⡎⠱⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢂⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⠁⠀⠠⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠈⢉⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⣳⣦⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠋⢡⣿⠁⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡦⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⡟⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠉⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⢤⣤⣶⡾⠇⠀⢿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣴⣯⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣟⡉⢩⣤⠴⠶⠦⢤⣤⣴⣦⡴⠶⠚⠿⢿⣦⡀⢀⣄⣴⣶⣶⣶⡾⠿⠿⢿⣯⡉⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠻⠿⣷⠀⠀⠀⠀⠀⠻⠋⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠙⠻⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⢀⣴⠾⠿⠆⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡀⠀⣰⣟⠋⠀⠀⠀⠀⣿⡇⠀⠀⠀⠰⠂⠀⠀⠀⠀⢸⡇⠀⣠⡄⠀⣤⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠈⠁⠀⣿⠀⠀⠀⠀⠀⠀⣿⣡⣴⢿⣧⢸⡆⢀⣴⠿⠷⢸⣷⣟⠋⠁⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠉⠀⠀⠀⠀⣿⡠⠀⠀⠀⢀⠀⣿⣿⠃⢸⣿⢸⡇⣾⣋⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠃⠀⠘⠳⣧⣴⣾⠟⠃⢸⡟⠀⠸⣿⠸⡷⠘⢷⣶⠆⢸⣿⠙⢷⣄⡀⠙⠻⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⣠⠶⠿⠛⠲⠦⡀
⠀⠀⠀⢸⠧⢂⣴⠶⠟⢤⠈⠢⣄
⠀⠀⠀⠳⠞⡿⢧⠴⣶⢶⡄⠀⡈⣆
⠀⠀⠀⠀⠀⠉⢻⡟⠻⠆⠀⠀⠂⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠉⢉⡦⠤
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡌⠃⣯⡄⠀⣀⠦⢄
⠀⠀⠀⠀⠀⠀⡸⠠⠐⠀⠰⠀⡀⠀⡎⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⠃⣸⡏⢨⡞⡁⠀⣠⠃
⠀⠀⠀⠀⠀⠀⡇⠀⢀⠘⠀⢀⠹⣤⢡⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢻⣿⣦⢿⣟⣹⣟⢴⡎⣡⠓⣤
⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⢁⠀⡀⢈⣀⠳⠱⣄⠀⠀⢀⣀⠤⠐⠒⠫⡅⠀⠨⡀⠈⡾⠙⡿⠃⠀⡰⠋⣠⠏
⠀⠀⠀⠀⠀⡜⠠⠐⠁⠀⠀⡀⠙⡀⠙⠂⣠⣤⣥⣽⢷⣖⣲⣜⢁⣻⣠⣶⣶⠛⢷⣄⠹⠄⡀⠉⡠⠞⣁⡼
⠀⠀⠀⠀⠀⡃⠠⢰⠄⠘⠀⣘⣴⣿⣷⣾⣿⢿⠿⠉⠁⠈⠉⠛⠷⢾⣅⣀⠐⣀⣀⠉⣄⣈⣡⣤⡔⠚⣩
⠀⠀⠀⠀⠀⣇⣀⠋⠀⠀⠰⠟⠛⠉⠊⠀⠀⠀⠀⠀⠀⠀⠠⠸⢁⠠⣈⠿⣿⣃⣀⣐⡒⡈⣿⣿⣗⡡⠞
⠀⠀⠀⠀⠀⡇⠁⠸⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠅⠀⠀⠠⠀⠒⠈⢁⠉⣀⠄⣽⣿⣿⣿⣿⣿⣯⣿
⠀⠀⠀⠀⠀⠏⠠⠄⠀⠠⠀⣬⣙⡂⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⣠⠍⠈⠵⠀⠀⠘⢿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠘⠻⣿⡿⣤⣀⡀⠀⠐⠀⠀⠀⢥⠴⠂⣰⣒⠀⠀⠀⠁⠸⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢀⢀⠈⠛⢿⣿⣛⠀⠀⠀⠀⠀⠠⠰⢦⣍⡀⠁⠂⠠⢀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢳⡈⠒⢀⠀⢌⡧⠀⣺⣿⣿⣷⣦⣉⡉⠋⠈⢓⠮⣍⣛⣒⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣠⣍⡐⣦⣬⣷⣿⣿⣿⣷⡬⠙⠿⢶⣦⣴⣶⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣯⣿⣿⣿⣿⣿⡟⠙⡆⠀⢨⡙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⡆⠁⠰⢤⣀⣰⣶⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⡽⠿⠟⠙⢿⣦⡙⠛⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣐⣋⣐⣒⡛⠁⣚⣀⣰⢀⣐⢀⠉⠰⢢⣤⣤⣤⣄⡀⠤⠀⠠⠀⠤⠄⢀⣀⢀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠯⠝⠛⠩⣷⣼⣿⡿⣿⣯⣼⠟⢠⡧⠭⠭⠍⠽⠛⠛⠋⠉⠙⠋⠀⢀⣀⠹⠷⢶⣞⣛⡀⠈⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠶⠶⠖⣀⣠⣤⣄⠢⠶⠾⠬⠭⠭⠭⠐⠓⠚⠃⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⠀⠀⠈⠉⠁⣔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⡟⢛⡾⠿⠿⠿⠷⠿⠿⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣪⡵⣿⣺⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⢗⣈⣰⣿⣿⣷⣥⣌⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⠉⠀⢈⠓⣮⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⠛⣈⣁⠀⡤⢼⣍⣌⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢠⢠⢂⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢿⢠⠀⡤⢀⠈⠀⢉⠾⠉⢿⠁
⠀⠀⠀⠀⠀⠀⡠⠌⡢⣠⡥⢟⠎⢊⡱⠰⠎⠱⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣏⢋⣰⠂⠒⣀⣦⡝⡣⡂⡤⠞⡀
⠀⠀⠀⠀⠀⣒⣊⣱⡶⢛⡊⣠⠴⡟⢔⡂⠡⠊⠁⠙⢉⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢯⡱⢯⣍⠁⣈⠀⠤⠿⡎⠀⡥⡔⢧⡇
⠀⠀⠀⠀⠀⣍⢤⣿⠥⠐⡾⢓⢍⠞⠃⠀⠠⠀⠀⠀⢀⠁⠡⠿⠛⢷⠲⠶⣦⣤⢤⣦⢾⡿⢿⢳⣾⡑⠒⢌⡁⠤⢠⠶⠀⢘⣀⣂⣴
⠀⠀⠀⠀⠀⢠⠘⡗⢂⣹⣋⣅⡤⢉⠄⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣤⠀⣌⡁⢁⣘⣩⢟⢻⡿⢘⡉⠆⠡⢞⡁⢉⣨⠿⡏⢁⣸
⠀⠀⠀⠀⠀⠀⠆⠘⢉⣻⡄⣤⡠⠀⠀⠀⠀⠄⠂⠀⠀⠠⢀⡀⠈⠀⠀⢈⡷⠋⠅⠠⠁⣭⠢⡀⢈⡀⠀⡀⠒⢀⡁⢞⢳⠺⠛⢯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣆⡝⢳⣖⢀⡀⠐⠀⠀⠀⢠⣀⡈⠀⠘⠁⣈⡟⠁⠐⠀⠄⠀⠀⠁⠄⠈⡈⠓⠀⢁⢢⡐⢌⣡⣿⡀⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣞⡼⣿⣡⠊⠀⠀⠦⣀⡀⠄⢀⠀⢼⣿⠾⡃⠁⣔⢂⠃⡀⠀⠀⠀⠠⣘⣷⣿⠀⢙⣠⠦⡌⢶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⣋⠐⠒⠀⠀⠂⢄⠸⠰⠠⡾⠁⣿⢠⢋⠜⠑⠧⢖⣂⣀⣲⡶⣟⡣⠴⠆⠘⣧⢔⢁⡸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⢸⡧⡍⢠⡤⠀⣷⣂⡶⢬⡳⣬⡻⣷⣾⣿⣷⣾⠿⢻⠯⢅⣮⠔⠣⢀⠀⡀⢀⠠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⣿⣶⠟⢷⡶⠿⠙⢧⡜⠛⠋⣹⣭⠉⢡⠟⡤⡳⢫⣔⠼⣧⣠⡉⠊⢔⣄⣈⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢶⡆⠄⢓⢁⠘⠐⠆⠀⡁⠈⡁⢀⡘⢆⢹⡲⠚⢱⡙⢎⠃⣼⣫⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢿⣿⣤⡈⠠⠚⠀⢤⠝⠀⠀⢚⠡⠄⠘⠚⣴⢯⣾⣶⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣯⣀⠒⠑⢎⡱⠄⠆⠺⡽⣶⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⣿⣯⠐⠛⠶⢏⢄⠳⣐⣶⣿⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣓⠘⣋⢒⣳⣽⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠟⠉⠀⢻⣯⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣬⡏⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⣀⣀⡀⠀⠀⠀⠀⠰⠋⠹⠲⠿⠷⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠺⣿⠿⠖⣶⠶⠄⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⢀⣤⣀⠀⠈⠁⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁⠀⠀⠀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⣴⣿⣿⣿⡆⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠒⠤⣀⣀⣀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠛⠿⠿⠛⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡼⠀⠀⠀⣀⣤⡤⠤⠶⠤⣄⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⢺⡆⠀⠀⠀⠀⠀⢨⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠇
⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠐⠒⠒⠒⠒⢠⡀⠀⠀⠀⠀⠀⢀⡤⠼⠧⠤⠤⠤⠤⠤⠼⠼⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠃
⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⢀⣀⡠⠤⠔⣊⡅⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂
⠀⠀⠀⠐⢬⠭⠉⠉⠭⠭⠁⠤⠐⠂⠉⠀⡂⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠘⡄⢀⣀⣀⡀⠤⠤⠀⠐⠒⠈⢹⠀⠀⠀⠀⢀⣇⣀⣀⣀⣀⣀⢀⣀⣀⣀⠀⠻⣃⣟⠘⠃⠀⣠⠒⠢⠤⠭⠍⠉⠐⢲⠋⡇
⠀⠀⠀⠀⠘⡄⠀⠀⠀⣠⣤⣦⣄⠀⠀⠀⢸⠀⠀⠀⠀⠓⠐⠒⠀⠀⠀⠐⠒⠒⠒⠒⠒⠐⠀⠐⠃⠀⠀⡇⠀⠀⠢⠠⠐⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⢱⠀⠀⠰⣿⢿⣽⣿⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠁⢀⡀⠀⠠⠤⠤⠄⠚⠃⢰
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠙⠻⠟⠋⢀⣀⠠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⣔⡉⣑⢏⡠⢶⠀⠀⠀⠀⠘⠁⢠⢰⡴⠄⠶⠦⠀⡇⢠
⠀⠀⠀⠀⠀⠀⠐⢖⠒⠒⠂⠈⠉⠀⠀⠀⡄⠀⠀⠀⡠⠠⠤⢊⠭⠠⠕⠀⣈⠔⠨⠥⠄⠒⠤⠀⠀⠀⠀⢰⣈⡡⡀⠤⠤⠤⠤⠒⠃⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠄⣀⠀⠀⣀⡠⠄⠊⠀⠀⠀⠀⡗⢒⡒⢁⠔⠒⠊⠀⠀⠀⠀⣀⠀⠀⡀⡀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢰⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠓⠂⠑⢊⣐⢂⡮⠭⠱⢞⢄⡨⠮⡀⢴⠀⠀⠀⠀⠆⠀⠐⠒⠂⠀⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠐⠠⣀⠀⠀⠀⠀⠀⢸⣁⢉⡈⡡⠤⠤⠊⠑⠒⠉⠑⠀⠒⠢⠼⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠈⠐⠠⢄⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢀⠤⡐⠜⠋⠁
⠀⠀⠀⠀⢀⠴⠈⠠⠤⠤⠄⠤⠤⠤⠤⠄⠤⠤⠤⠬⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠄⠧⠤⠶⡈⢁⡀
⠀⠀⠀⠀⠘⣷⣮⡴⡤⠰⢶⣤⣤⣄⣄⣠⣡⣤⣐⣲⣶⠃⠀⠀⠀⠀⠀⠀⠀⣔⠈⡡⠄⠰⡀⠠⡤⢀⣐⠢⠤⣄⡉⢲⡄
⠀⠀⠀⠀⠀⢏⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⢋⡁⠃⠀⠀⠀⠀⠀⠀⠀⢙⠛⠠⠬⢵⣏⣘⣏⣁⣬⣡⠦⠶⠚⢛⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀⠀⠀⠀⠀⠀⣀⣠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠃⠏⢇⢠⠖⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢸⠇⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢀⡞⠀⢸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠈⠀⠀⠈⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠨⠀⡄⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢖⠀⠂⠀⢀⠀⢰⠀⢠⠀⠀⣼⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣒⠶⠤⢤⣀⣀⣤⠤⠴⠖⠂⠐⠋⠱⣩⣿⣦⠀⠰⠸⡄⠀⠃⠀⠋⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠁⠀⠀⠀⠀⡤⠞⠀⢇⠿⢿⡁⠀⠘⠁⠙⢆⠀⠀⢰⣾⡧⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢴⠖⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢤⣀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠈⠩⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠔⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠾⠃⠀⠘⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠐⠀⠀⠀⢀⢈⡓⢦⡀⠀⠀⣧⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠁⠀⣀⠀⠀⠀⣣⠀⠀⠐⠶⠖⠀⣂⠀⢘⠳⠲⣄⠙⢄⡀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀⠀⢠⠎⠀⡼⠋⠀⠁⠀⠀⣞⡀⠀⠉⠛⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠰⡇⠀⠀⠀⠀⠼⠀⠀⠀⠈⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡃⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠹⡆⡞⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠊⠀⠀⠀⠀⠀⢐⡅⣠⣠⠆⠀⠀⠈⢇⠀⠀⠀⠀⠀⣀⠴⠻⠈⠃⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠀⠀⠀⠀⠀⠀⡄⠈⠁⠀⠀⠈⠀⡄⠈⠑⠦⠶⠖⠋⡅⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠈⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠠⠀⠂⠀⣠⢀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠴⠂⠀⠀⠀⢀⡄⠀⠐⠣⠋⢀⣾⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠄⠀⠀⠀⠈⠁⠀⡴⠀⢀⠎⠀⠀⣠⠟⠀⠀⠀⠀⠀⠸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠔⠂⠸⠤⠀⠈⠰⠖⠋⠁⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢊⠀⠀⠀⣠⠎

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⣠⣤⣾⣴⣦⡤⠞⠃
⠀⠀⠀⠀⠀⠀⡻⣿⣟⣳⣖⠙⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠂⢀⣀
⠀⠀⠀⠀⠀⠀⠐⣿⣹⡿⠁⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⢀⢶⣠⢶⣭⡴⠶⠌⡻⣄
⠀⠀⠀⠀⠀⠀⠀⣹⠃⠀⠀⠀⠀⠐⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢂⣠⣖⣛⣵⣿⣿⣷⣾⣿⣶⠙⠳
⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠐⡏⠇⠀⣀⣀⣀⠀⠀⠀⢀⣠⣼⠿⣝⠏⢯⣵⣽⠲⡦⣌⠻⠦
⠀⠀⠀⠀⠀⠀⣼⡄⠠⢆⡀⡀⠀⣿⣿⡘⠛⠛⢛⡉⡿⣵⡾⠿⡛⠟⠛⣮⣧⣼⡋⠙⠻⣦⣯⡙⡄
⠀⠀⠀⠀⠀⠀⡿⠀⠀⢸⣿⣇⣴⠿⡝⠃⣐⣤⣷⣉⣕⠀⠉⠐⠺⡛⠻⢽⣿⣏⡙⣦⣄⠈⣿⣹⣮⠉
⠀⠀⠀⠀⠀⠀⢷⡆⢀⠀⠙⡟⣿⡆⠓⠀⠙⢠⢋⢿⡛⡥⠷⡧⠲⡌⡹⣦⣻⣷⣿⣿⣿⣇⢿⢸⡿
⠀⠀⠀⠀⠀⠀⠘⢿⣿⠇⣴⣷⣿⣧⣾⣴⠆⣢⠸⠇⠱⠦⠔⠂⠠⠀⣱⣏⢡⣿⣿⣷⣿⡏⠸⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣷⡸⣇⠙⠻⠹⢯⣑⠸⠉⠃⢰⠯⠀⠀⠐⠀⠑⣸⡍⣯⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡙⠀⠀⡀⠹⠯⠀⢀⣰⠟⢳⠒⠒⠒⠀⠐⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣬⣴⡐⢸⣿⢄⠀⠸⠠⡄⠀⠀⢼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣺⣧⣄⣄⢁⣗⢦⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⡿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠏⠄⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⢀⢁⠀⢀⠀⢸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠁⠀⢀⠋⠛⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠢⡀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠘⠁⠀⢱
⠀⠀⠀⠀⡐⠉⠈⠑⠃⠀⠀⠐⠀⠐⠀⠘⠂⠢
⠀⠀⠀⠀⢃⠀⠀⠄⠀⡀⠀⠀⠁⠀⠐⠀⠀⠸
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠈⠣⣀⠠⠀⠀⠀⢀⠀⡐⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⠖⠉⠀⠀⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⡀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠢⡀⠆⠈⠀⢠⠀⡠⠊⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢀⢀⠠⡙⠁⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠇⠀⠘⢨⠖⠁⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⢆⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠈⠢⠀⠀⡄⠂⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢈⠈⠈⢀⠕⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⢀⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠌⠁⢺⠁
⠀⠀⠀⠀⠀⠀⡀⠔⠃⠀⢀⣀⠀⠀⠀⢀⣀⠀⢀⠇⠈⡡⢊⠒⠤⢀⡀⠀⠀⠀⢀⡀⣤⠒⠈⠀⢀⡀⢸
⠀⠀⠀⢀⡴⠊⠀⠀⠑⠊⠁⠀⠑⠤⠤⠃⠈⠁⠁⢀⠜⠀⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠆⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠸
⠀⠀⠀⢇⠀⠀⠀⠀⢰⠀⠀⠀⠢⠂⠀⠀⠐⠀⠐⡀⠈⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠹⠂⠀⠀⠈⡄⠐⠀⠀⠀⠐⠀⠀⠀⠀⠉⠒⠂⠉⡇⠀⠀⠀⠀⠈⠠⠀⠀⠂⠆⠀⠀⠀⠰
⠀⠀⠀⢠⠁⠀⠀⠀⠀⠰⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠐⠂⣡⠙⠢⠀⠠⠊⠀⠀⠐⠀⡆
⠀⠀⠀⠀⠂⠄⠠⠄⠀⠀⢣⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠱⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠤⣀⣀⠀⠀⠀⠀⠀⢀⣀⠠⠠⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠉⠀⠈⠀⢹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⡀⠀⠀⠀⠘⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢔⠅⣕⣀⣠⣔⠧⢨⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠂⠀⠀⠀⠘⠃⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣶⣿⠟⠁⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠈⠉⠀⠀⠀⠀⠀⢿⡿⠿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄
⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄
⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆
⠀⠀⠀⢰⣿⠋⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠘⣿⣆
⠀⠀⢠⣿⠏⠀⠀⠀⠀⢠⣟⠙⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⢹⡆⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⣼⡿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠃⠀⠀⣠⡴⠖⠶⣄⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⢀⡴⠋⠀⠀⠀⠙⢷⣄⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣅⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⣀⣠⣤⣤⣤⣄
⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢿⣷⡿⠟⠛⠉⠉⠹⣿
⠀⠀⠈⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⣷⡀⠀⠀⠀⢸⣿
⠀⠀⣼⡿⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠀⠀⠀⠈⢿⡀⠀⢀⣿⡏
⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠾⠿⢿
⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣼
⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆
⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⡿⠟⠁
⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⡀⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠈⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣶⣦⣤⣶⡿⠏
⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⠿⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⠿⣿⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠈⣿⣍⠉⠉⠉⠉⠉⠉⠁⣠⣿⠟⠀⢻⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠁⠀⠀⠈⠙⠻⢷⣦⡀⣠⣶⠿⠛⠁⠀⠀⠀⠈⠉⠛⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣴⣶⠾⠿⢶⣶⣦⣤⣼⡿⣿⣧⣤⣤⣶⡾⠿⠿⠷⣶⣶⣶⡿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣄⢀⡰⠀⠐⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⠉⠀⠀⠀⠀⠈⢇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠈⢉⠙⢲⡤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠈⠀⣏⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢄⡀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⣀⣀⣉⠑⠢⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠉⠉⠉⠉⠁⠠⣤⢿⣄⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⣰⠋⠀⢀⠄⠂⠈⠀⣀⣀⣀⠀⠈⠠⠙⠷⣤⣤⣤⠶⠛⠁⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠞⠋⠉⠁⠠⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⡆⠀⠀⠀⠀⠀⢸⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠠⠒⠉⠁⣀⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⣇⡜⠀⠀⠀⡄⠀⠀⡆⢁⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠉⠉⠹⡆⠀⠀⠀⠀⣀⣤⢊⣀⡄⠀⠀⠀⠀⠀⠉⠀⠀⠀⣸⠁⢀⠜⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣈⡭⠝⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠁⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⢀⣀⡠⠀⠀⠀⠀⠀⢀⣠⡴⠛⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⠶⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠒⠁⣀⡴⠟⡡⠶⠚⠛⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠛⠛⠲⠮⣙⠳⢦⣤⣀⣒⣒⣒⣒⣛⣋⡉⠉⣀⣠⡤⠖⠛⣉⣀⣤⣤⡴⠶⠶⠶⠶⠦⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠩⠭⠭⣭⣥⣤⣬⣭⠥⠶⠖⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠲⠶⠶⠶⠤⠤⠴⠶⠶⠖⠒⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀⣤⣤⣄⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⠀⣀⣀⠤⠄⠒⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⡔⢲⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠌⠓⠲⢄⠀⡀⠤⠒⠒⡲⠦⣀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠋⠀⠑⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⠁⠀⠀⠀⠀⠀⠘⣦⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⢠⠀⠀⠀⢻⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡄⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠠⠀⠛⠺⡄⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣽⠀⠀⠀⠀⠀⠀⠀⠀⣈⠃⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⣀⡀⣀⡀⠻⠗⠀⣣⠈⠀⠀⠀⠑⠄⣀⢀⠀⠀⠀⠀⠀⣴⠋⠊⢉⠉⠣⣀⠀⠀⡀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠐⠁⣠⢄⠹⢶⠤⠾⠃⠦⡀⠀⠀⠀⠀⠀⠈⠑⠂⠄⣰⣾⡀⠀⠀⠈⠀⠀⡤⠑⠛⠀⠀⠀⠀⠀⠀⠈⠓⠄⣀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠠⣀⡩⠞⣼⠁⠀⣠⠀⠘⢂⡤⠐⠒⠀⠐⠒⠠⢄⣹⡞⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠇⠀⡠⠄⠠⣄⠸⡀⣶⢌⢁⣠⡞⠉⣠⠀⠐⠀⡒⠀⠀⠀⠉⢧⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⢸⡆⢧⣅⣀⢀⡀⠀⠀⠈⠣⠈⠀⠁⠔⠁⠀⠀⠈⣳⣦⠤⢀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠥⠎⠀⡟⠁⠀⠈⡇⠀⣀⡈⠁⠀⠀⠀⠐⢂⠨⠓⠝⠋⠀⠀⠀⠀⢘⠀⡠⠂⠀⠀⠉⠒⠤⠤⣀⠀⠀⠀⠠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⣇⠸⠖⠀⣣⠀⠀⠤⠂⠀⡐⠠⡜⠁⠀⠀⠀⠀⠀⠀⠀⢀⡶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠾⠀⠓⠒⠒⠙⢄⠀⢂⠀⠀⠰⠀⡀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⣡⠀⠀⠀⠤⠐⢞⠈⠑⠤⣀⣀⠀⣀⣳⡀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢿⠁⠁⠀⠠⣄⠀⠀⠀⠀⠀⢨⠀⠀⠈⠢⠵⠀⣠⣄⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢀⡀⠀⠉⠉⠳⠂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠈⠐⠂⢤⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠀⠀⢀⣀⠤⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡴⠉⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠐⢄⣀⣀⣀⠠⠜⢗⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣁⠠⠊⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⣠⠴⠖⠒⠉⠀⠀⠀⠀⠀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠉⠉⠉⠁



⣿⣿⡿⠿⣿⡿⢿⢿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣶⣴⣿⣷⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣶⠀⣿⣠⣶⣠⣄
⠀⣀⣾⠿⡝⠉⢁⣩⡼⣿⣿⣧
⢰⠏⠙⠀⣠⣶⠶⠿⢿⣶⣿⠃
⡴⠀⢠⣶⣿⣿⣿⣶⣦⢈⠉⠙⠦⣄
⠰⣤⣿⣃⡉⢹⢿⣿⣧⡞⣧⡄⠀⠈⢓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣼⡜⢿⣿⣿⣤⣿⣿⡭⣡⠿⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣷⡄
⠉⠀⠀⣧⣿⣿⣿⣠⡖⠏⠀⠀⠀⠀⠀⠀⠀⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣯⣭⣷⣾⣷
⠀⠀⠀⠹⣌⠿⣾⡟⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⢛⣋⣥⡴⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⣿⡟⠀⠂⢀⠀⠀⠀⢀⠃⠀⠀⠐⠀⠛⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠻⢾⣻⠿⠏⠋⠙⣠⣾⣿⣿⣿⡟
⠀⠀⠀⠀⢰⡟⣀⡀⠐⡀⠠⠆⠂⣌⢀⢠⠄⡠⠄⠀⠄⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⠤⠤⠤⠤⣴⡖⠋⠁⠀⠀⠀⠀⠚⠻⠟⠛⣩⣦⣿⣿⣏⣀
⠀⠀⠀⠀⠘⣿⡁⠀⠀⠁⠀⠆⠐⢫⡈⠓⠄⠀⠐⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠉⣠⡀⢰⡿⣽⠟⣿⣿⡋
⠀⠀⠀⠀⢸⡟⠏⠀⠀⠀⠈⠠⢛⠨⠀⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⢀⣀⡀⠀⠀⠀⠠⠀⠀⣀⣀⡀⠀⢿⣿⠿⢁⣤⣶⣿⡿⠃
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⣦⣀⡀⠈⠀⠀⠀⠀⠀⠀⠈⣉⠓⠀⠀⠈⠀⠟⣿⡟⠁
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠛⠿⣇⣀⠀⠀⠤⣄⡀⠀⠮⠟⠂⣴⠖⢤⣿⡟
⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⢀⠁⠀⠀⠀⢀⠂⠀⠀⢀⠀⠀⠈⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠐⠻⠆⠀⡀⠉⠉⠢⠄⡈⠙⠲⠒⡶⠦⣀⣒⣊⡿
⠀⠀⠀⠀⠀⠀⠘⣿⣦⡆⡀⠃⠈⠀⠀⠀⠀⠀⠂⠈⠑⢆⣉⣶⣄⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠘⠦⠀⠀⠰⣄⠐⢷⣦⣌⢻⣍
⠀⠀⠀⠀⠀⠀⠀⠹⣿⠙⢿⡄⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⣍⡉⠓⠀⠑⠀⢘⠷⠀⢀⣀⣠⣤⡶⠶⠳⠴⠶⠶⢶⣶⣶⣴⣿⣶⡄⣍⣽⡿⣹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣠⡀⠀⠀⠀⢀⠀⢄⠀⠑⠀⠈⠀⣀⠀⢄⢀⡀⣀⡸⠇⠋⠘⠉⠛⠛⠛⠛⠛⠒⠒⠶⠤⠤⠤⣤⡄⠙⠻⢿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣍⠂⠀⠠⠀⠁⠀⠀⠀⠂⠀⠐⠁⠀⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠬⠁⠀⣠⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣗⢤⣦⡀⢘⠲⣄⠀⠤⠀⠀⡀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⣯⣳⣎⡂⠈⢄⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠈⠃⠀⠀⠀⠀⠀⢔⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢿⣶⣄⠀⠒⢤⡀⠐⠀⠁⠀⠀⠀⣀⡀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠐⠂⢾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⣤⣢⣤⡀⡑⠀⠁⠢⠀⠀⢶⣤⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⢀⣀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡰⠿⠿⣿⣷⣾⡿⠆⣤⣀⣳⣀⠀⠀⠀⣀⠁⠠⣄⠀⠘⣁⣤⡶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠹⠛⣿⣿⣿⣿⣿⣏⣁⠘⢀⠠⣴⣤⣽⣶⡼⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⡀⣠⣀⣸⣶⠿⠋⠙⠛⠻⠿⢿⣦⣤⣽⣻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⣻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢣⣄⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣴⡶⣦⣾⣷⢟⣼⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⡟⡊⢠⠿⠿⠗
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣻⣷⣚⣁⣈⣉⣉⣀⣀⣀⣀⣀⣀⣟⣻⣿⣛⣛⣛⣒⣺⣿⣵⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠲⡄
⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⡰⠁⠉⠠⠐⠚⠯⣍⠛⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢠⠇
⠀⠀⠀⠀⡇⢠⠀⠀⠀⣤⠀⠈⣧⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⡾⢳
⠀⠀⠀⠀⠘⠧⣄⠀⠘⠟⠀⠀⡜⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢈⡄⠀⢠⠴⠊⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠶⠶⠶⠒⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡞⡆
⠀⠒⠒⠁⠀⠀⢀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⢀⠄⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⣀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡆⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⠀⠀⠀⣿
⠀⠀⠀⠀⠓⠒⢨⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢶⣋⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡷⠀⠀⡟
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡇⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠸⣤⠆⡀⠀⠀⠀⠀⡄⠀⠀⠀⠑⠛⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡄⠀⠀⡦⠃⠀⠀⠀⠀⠀⠀⠙⠢⢀⠗⠒⠲⠤⠴⠒⠒⠒⠉⠀⠀⠀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠶⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡗⢲⠒⠒⠒⠒⠊⢹⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢧⣀⡀⠀⠀⢸⡆⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠒⠈⠀⠀⢀⡠⢭⡵⠤⠜⠁⠀⠙⠒⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠁⠂⢉⠃⠀⠁⠀⡳⢂⠤⠰⠄⠀⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠘⠋⠀⠀⢮

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡠⢶⠿⠿⠆⠶⠶⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡖⠂⠰⠛⠈⠛⢛⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⢤⣀⣠⣄⣠⣄⢀⣀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡧⠀⢀⣠⣴⣾⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠿⠛⠛⠛⠋⠈⠉⠙⠛⠋⠙⠉⠛⠻⠆⣤⡄⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠛⣫⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠉⠠⣦⠀⠀⠀⢀⣴⡄⠀⠀⠀⠘⠿⠂⠀⠀⠀⠀⢀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡍⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋
⢠⣤⣶⣤⣀⣴⡶⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⣀⠀⠀⠀⠀⠀⠀⣯
⣈⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠶⠿⢷⣤⣤⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⢀⣿⡆
⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⢸⣿⣭⣶⠶⠮⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠁⠀⠀⠀⢀⣼⡟
⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⣛⣛⠛⠷⢤⣴⣶⠆⠀⠀⠀⣀⣤⡄⠺⠛⠉⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⣉⣉⣭⣤⣶⣶⣶⣧⣤⣴⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟
⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠉⠛⠛⠉⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⢀⢠⣤⣿⠟⠃
⠀⠀⠀⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⣯⠤⠆⠀⠀⠀⠀⣰⣿⠉⠉
⠀⠀⢸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣤⣦⣤⡾⡿⠇
⠀⠀⠀⠉⣿⣷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⠛⠉⠉⠀⠉
⠀⠀⠀⠀⠘⠋⠉⢉⣴⣶⣤⣄⣀⠀⠀⠀⠐⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠙⠛⠂⠰⢄⣴⠟⠉⠀⠀⠀⠀⢀⣀⢀⣀⢠⣴⣶⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⣀⣀⣴⠟⠻⢮⡉⠛⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡄⠀⢼⣿⠋⠁⠀⠀⠀⠙⢦⡈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠘⣧⠀⠀⠀⠀⠀⠀⠀⠹⣦⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠘⣷⡀⠀⠀⠀⠀⠀⠀⠈⢷⡌⠻⣦⣄⣀⣀⣠⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡘⣷⡀⠀⠀⢀⣤⣤⡴⢾⣃⣄⡀⠨⣙⣻⣿⣶⣾⠿⠟⠻⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡈⠻⣄⡀⠘⠛⠛⠚⠉⠉⠉⠉⠓⠶⣯⣭⣛⠾⢯⡛⠋⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠇⠀⠈⠻⣿⣓⣀⣛⣛⣿⣽⠿⠷⠀⠀⠀⠉⠛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣚⠉⣥⡶⢦⡄⢶⣤⣤⣤⣉⣉⣉⣉⣋⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉⠀⠀⠀⠈⠻⣆⡙⢦⡀⠀⠀⠉⠉⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣶⢶⡀⣠⠞⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⡙⢷⣿⠈⢻⡏⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠛⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠛⠛⠛⠛⠛⠛⠛⠓⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣸⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠸⣇⢀⣿⠁⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⣀⣤⣬⣭⡉⠁⠀⠀⠀⢹⡄⠸⠀⠀⠐⠆⢀⡾⠁⠀⠀⠀⠈⢉⣭⣤⣤⡀⠀⠀⠀⠀⢸⣧⣀⣀⣀⣠⣤⠶⠶⣤
⢿⠀⠀⠀⠀⠀⠀⠙⠛⠟⠛⠁⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠙⠛⠟⠛⠁⠀⠀⠀⠀⣾⠁⠈⠉⠉⠁⠀⠀⠀⢸
⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡷⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⣯⠞⠁⣠⣏⡀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠞⠋⠁⠀⠀⠀⠀⠈⠉⠙⣧⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠲⡶⠶⠶⠶⠶⠒⠒⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣯⡀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⣤⣤⡤⠶⠋⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⢶⡶⣶⠶⠶⠶⠶⠶⢶⡾⣟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣥⣿⡀⠀⠀⠀⠀⣼⣥⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⢿⡇⠀⠀⠀⢸⡟⣿⢿⣇
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣿⣶⣷⣶⣶⣶⣾⣶⣿⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣦⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⡍⢏⣛⣚⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⡾⠉⠛⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣇⠰⠛⠀⡟⠣
⠀⠀⠀⠀⠀⠀⣰⠷⣟⣛⣟⣛⣶⣤⡔⠨⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢣⢛⣸⣿⣦⠀⣽⣾⡄
⠀⠀⠀⠀⠀⠀⠵⣞⣭⣥⡖⢋⣡⣤⣼⣷⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠐⠉⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⢹⠋⣤⣿⡿⠟⠛⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡀⡵⣶⣿⣿⣿⣿⡿⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣿⣯⣷⣖⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⠛⢮⠲⣿⣿⣿⣿⣿⠃⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣷⠊⠻⣻⣿⣶⣤⣀⣤⣠⣞⣛⣹⣧⠨⣵⡾⢧⣿⣿⣿⠿⠁⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡿⢩⢖⣛⣭⣾⣿⣴⣬⣿⢯⡀⠂⠈⠀⢉⣿⣾⣏⣿⡠⣿⣿⠟⠀⠀⠀⠀⠤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⣿⣿⣯⡕⣻⣻⣿⣇⣀⠁⠀⠀⠀⠀⠀⠈⢷⣯⣹⣾⣿⠆⢐⠀⠀⠀⠘⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣿⢞⡟⣿⠟⡹⣻⣿⣿⣿⣤⣡⣶⣦⣤⣥⣀⣵⣿⣿⣿⠋⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⣿⣿⢣⢨⠞⠉⣽⣿⣿⡿⣿⣷⣿⣿⣿⣿⣿⡿⠛⢀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠯⠿⣽⣟⣴⣾⣿⣿⣿⣿⣿⣿⣿⡟⠛⠏⠉⠢⠄⡂⠀⠀⠀⣤⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠐⣣⠟⣴⠈⢡⣢⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢐⣫⣞⡿⡷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⢹⣶⡞⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⠘⡿⠍⠉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢽⠒⠃⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣯⣽⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⢀⣠⣀⢹⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠈⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⣶⡬⠉⠉⠀⢀⡙⠄
⠀⠀⠀⠀⠀⠀⠿⠅⢁⡀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠻⣿⣶⣾⣿⣿⠛⠛
⠀⠀⠀⠀⠀⠀⠘⠧⣄⢀⡄⠀⠂⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⢫
⠀⠀⠀⠀⠀⠀⠀⠲⢿⣿⣿⡶⠆⠀⠶⠆⠲⠀⠀⠛⡻⠷⠶⠶⠢⠤⠤⢀⣀⣀⣀⣀⣀⣀⡤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠹⣄⡀⠀⠄⠀⠀⢠⠸⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣨⠷⢦⣤⣈⣙⠂⠀⢤⣠⣼⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣽
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣤⣉⡙⠓⠀⠐⣿⠋⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣏⣓⠀⢠⣾⠂⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣀⠼⠗⠀⢶⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⡖⠀⠈⠳⡦⠀⠀⡠⠔⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⠴⠚⢷⣖⠊⢀⣀⡀⠀⠀⠂⠀⠀⢀⠀⢀⡤⠄⠀⠀⠀⠀⠀⠀⢀⡄⠠⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣣⡀⠀⠀⠀⡉⠉⢉⠈⠉⠉⠀⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⠉⣮⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡅⡠⠊⢈⠁⠀⠢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣯⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡤⠂⠀⠀⠀⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⣤⡶⠙⣾⠻⠀⠀⠀⢀⠀⠀⠀⠔⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣾⣧⣀⡶⢠⣶⢀⠈⠀⠈⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣶⣷⣿⣄⣤⣤⣤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡈⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠈⢿⣿⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠀⠃⠀⠀⠀⢀⣠⣿⣿⣦⣜⣿⣷⡄⣀⣀⠀⠀⠴⠀⡀⠀⠀⢠⡜⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⢀⣀⣑⣢⡀⠛⣿⣤⣤⣤⣈⣉⣉⣠⣠⠿⠿⠛⠻⠷⣿⣿⣷⠶⠶⠾⠷⠄⠰⢾⣧⡰⡥⠀⠀⠠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠷⠀⠼⠛⠛⠣⠛⢿⣿⡷⠄⡀⠀⢿⡦⠀⠀⢍⠉⠀⣄⠀⢰⣰⣴⣾⡷⢳⣷⣶⡭⢿⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠒⠻⠃⠀⠉⠙⠛⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠚⠉⠉⠉⠉⠉⠓⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⣀
⠀⠀⠀⢠⡃⠀⠀⠀⠀⠀⡔⠉⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⣄⡀
⢀⡤⠒⠉⠉⢢⠀⠀⠀⠀⢧⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀
⢏⡀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠉⠉⢲⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⢲⡀
⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠚⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣱⠄⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣍⠉⠁⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠸⡒⠤⠄⡀⠤⠴⠊⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠤⠔⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠒⠲⠦⠶⠶⠒⠒⠒⡋⠉⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡜⠀⠀⠀⠀⠀⢠⠁⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠊⠀⢸⠀⠀⠀⢀⣀⠴⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠪⠭⢄⡤⠄⠀⢀⠤⣬⠖⠊⠉⣉⠄⠀⢀⠤⠤⠑⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠥⠤⠔⠊⠁⠀⠋⠉⣠⢋⣁⡠⠖⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠐⠊⠉⠉⠑⠄⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⠄⠒⠒⠂⠤⠄⡀⠀⠀⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⡈⠄⠒⠒⠀⠀⠀⠀⠀⠈⠑⢄⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠀⠐⢉⡠⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⢠⠒⠩⠌⡁⠒⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠈⠀⠔⠉⠀⠀⠀⠀⠀⠀⠈⠃⢀⠜⠠⢀
⠘⡄⠉⠂⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠈⠢⣀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⢔⠂⠈
⡌⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠉⢣⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⣸
⢣⠒⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⢠⠀⠀⠀⠀⠀⡠⠊⠡⠤⠓⠁
⡰⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠚⢄⠀⠀⢀⠎
⢇⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠉⡄
⠈⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡀⣁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠑⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠂⠉⠁⠀⠀⠀⠀⠀⠈⠁⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⡰⠀⡄
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡰⡠⢁⠌
⠀⠀⢃⠀⠀⠀⠀⠀⠀⡔⠁⠀⢀⡄⠀⠀⡠⠀⠀⠀⠄⠀⢠⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⣀⠄⡪⠊⠀⠸
⠀⠀⠈⢄⠀⠀⠀⠀⠀⠈⠐⠒⠧⠀⠠⢔⠁⢀⡠⢎⣀⠠⠆⡀⠠⠤⠄⠒⠈⠁⠀⠀⠀⠐⠉⠀⠀⢠⠃
⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠈⠐⠠⠤⢀⣀⠀⠀⠀⠀⠸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠄⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠤⠤⠤⠤⠖⠚⠉⠉⠉⠉⠲⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢀⡆⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⢰⡋⠀⠀⠀⠈⠋⠿⢠
⠀⠀⠘⢶⣌⣉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⠶⢦⣤⣀⣀⣠⡴⢞⡿⠓⢦⣀⠴⠊⠉⠉⠉⠙⠦⣄⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠈⠙⠛⣻⠃⠀⠀⠀⠀⢀⣼⡿⣡⣾⣋⠁⠁⠉⠙⠛⠉⢠⣯⣶⣶⣶⢿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⠤⠽⢦⡀
⠀⠀⠀⠀⠠⠄⠊⢁⠀⠀⠀⠀⠀⣼⣿⢁⣯⣶⣾⡅⠀⠀⠀⢀⣴⣿⣿⣿⣿⣏⠀⠀⢀⠤⣶⣶⢶⡦⢤⡀⠀⠀⠈⡍⠙⣯⠐⠂⢄⡀
⠀⠈⠳⠶⠶⠶⠞⣿⠀⠀⠀⠀⢰⣿⡇⢀⠙⠯⠟⣡⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡆⢀⣀⡀⢷⣭⣪⠅⠀⠀⡀⢀⡠⠴⠚⠓⠒⠒⢤⣑⡄
⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⢀⣿⣿⡇⠸⡄⠐⠚⠁⠀⠀⠈⢿⣿⡯⠭⠬⣭⣿⣷⡀⠀⠈⠙⠁⠀⠀⠀⣌⣠⠀⡀⠳⣾⣯⡀⠀⠀⠈⠁
⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⢀⣾⣿⣿⠁⢰⡇⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⣀⣤⡬⢽⢿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠙⣿⣷
⣀⣠⣴⣿⣿⣤⣤⣤⣴⣾⣿⣿⣿⠛⠀⡌⠁⡀⠀⠀⠀⢀⣠⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⢸⡏
⠈⠙⠛⠿⠿⠿⢿⣿⠿⠿⠟⠋⠁⡀⣰⢿⣆⠙⠿⢿⣿⣿⠇⢸⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢠⠀⠀⢰⠃⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⢸⣿⡆⠀⠀⠈⠿⠀⠘⡆⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠸⠀⠀⠈⢧⣀⠀⢀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⡿⢹⣇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣷⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⢈⠉⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡼⠁⣼⣿⣦⣤⣼⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡀⠀⠀⠀⠀⡇⠀⠀⢀⠈⢧⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠈⠀⢰⡟⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⡀⠀⠀⠀⡇⠀⣄⠈⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢀⡟⢰⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⢷⡀⠀⢠⠃⠀⠙⠀⠀⢦⠀⠘⢦⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠊⢠⡿⢫⣿⠟⣿⣷⣤⣀⣀⣠⣾⣿⣿⣿⣿⣿⣏⠳⠤⠊⠀⠀⠀⠀⡄⠈⠁⠀⠀⠳⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⢠⠟⠁⣸⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣆⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠠⣄⠀⠀⠀⠀⠹
⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠰⠋⠀⣰⠋⠀⣸⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠻⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢹⡄⠀⠘⣆
⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⢠⠟⢀⣿⠻⣿⠿⣿⡏⢻⡿⠸⡟⠘⣇⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠈
⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⣸⠃⢰⠏⠀⣿⠃⢸⡇⠀⡇⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠌⠀⠀⡟⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠶⠾⠟⠛⠻⠿⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡛⠉⠉⠉⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣆⠀⢀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⣴⠋⣠⡼
⠀⢀⣤⣶⡶⠾⠿⠿⠿⠿⠿⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠈⠉⠛⠻⣦⣄⣀⣀⣀⣠⣤⣴⡾⢋⡾⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⢀⡾⠀⠟⢡⡞⠉
⠀⠻⣿⣤⣴⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢰⡇⠀⠀⣀⣤⣾⠿⠛⠋⠉⠉⠀⠀⠀⠀⠰⠟⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣡⣶⢻⡇⣀⠀⢸⡇
⠀⠀⠀⠈⠉⢻⣷⣶⠶⠀⣀⣀⣠⡄⠀⠀⢻⣄⠀⢀⣿⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢻⢗⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⣳⠏⠀⢸⡇
⠀⠀⠀⠀⠀⠈⠻⣿⣿⠟⠋⣉⣁⡤⠀⠀⠀⣹⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠵⢂⠀⠀⠀⠀⠈⠋⠀⠀⠚⠋⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣟⣋⣩⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣉⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⢿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⣀⣠⣤⡶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠩⣽⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠈⠽⢖⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣾⣿⣧⣼⣷⠀⣤⡀⢀⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠉⡿⠋⠶⠂⢶⣠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣇⣸⡏⢀⣶⠀⣿⠀⣿⠀⢰⡄⠀⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠠⢤⣤⣤⡶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣾⡏⢸⣿⠀⣿⡀⢸⡇⠀⢸
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣀⣿⡇⢸⡇⠀⠈
⠀⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⢢⣶⡤⢀⠀⠀⣼⡿⠁⠈⠙⠛⠿⢾⣷⡀⣰
⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣾⣿⢟⣵⣿⢏⣼⡟⠁⠀⠀⠀⠀⠀⠀⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠶⣫⣴⣿⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧⣴⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣶⣦⣤⣽⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⣿⡟⠉⠛⠿⠷⣶⣶⣶⣶⣶⣦⣬⣝⡻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣯⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣦⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡎⠉⢉⣩⣿⣿⢿⣿⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠙⢿⣤⣀⠀⠀⠀⠀⠀⢀⣴⣾⣯⡴⠞⠛⠛⠶⢽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠿⠿⣧⠀⣾⠷⠾⠿⠿⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣶⣶⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠤⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢩⣤⠊⠉⠟⠯⣅⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣲⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡶⣤⠉⠛⢖⢺⠿⣶⡌⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠙⢥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠁⣺⣆⡸⠀⢈⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠖⠛⠳⠏⠁⠀⠁⠉⡔⠀⣄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠁⠈⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠡⠠⠘⠂⢀⠀⡄⠀⡠⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠂⠔⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢚⡲⢦⣤⠁⠂⢠⡁⠀⠀⠿⡄⢠⠀⢤⠀⠀⠀⠀⠀⢠⣀⢀⠀⡃⡴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⠠⢉⡤⠋⣀⠔⠀⠂⠐⢀⠔⡹⡊⠠⠔⠀⠀⠀⠆⠀⠙⠛⠓⢿⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠠⠤⢄⠹⠄⣘⣳⠀⡄⢁⠈⡠⢁⠚⡠⠈⡁⠀⠀⠠⠀⠀⠀⠀⠘⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⢈⡀⣉⣈⡃⠊⠄⠹⠐⡡⠀⠂⡖⢠⠃⠚⡀⠁⡠⡆⣤⠌⣢⠞⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⢋⢯⠔⣊⣡⠐⢣⠄⠼⢡⠀⠨⠐⠀⠐⠋⣛⣖⣀⠀⣲⣯⣥⠴⡏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⢙⣛⣃⣩⣍⡠⠠⠄⢀⠀⠀⠂⠀⠀⠐⠉⢿⣿⣣⣿⢱⢿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡗⠐⢂⣿⣥⡈⠤⢶⢧⣈⠐⠁⠀⠀⠀⠀⢀⠀⠙⢂⠛⢉⡍⢀⢼⣀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⡓⠺⠭⠭⣢⠁⣀⠄⠐⠀⠀⡀⠀⠀⢀⠀⡅⠀⢚⠖⣩⢃⡴⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣴⡟⠃⣈⣠⢄⠀⠀⠀⠀⠀⠀⠌⠀⠰⠀⠡⠋⠡⣁⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣧⣴⣭⣴⣄⡀⣠⣛⣨⣌⣂⣥⠋⣠⣦⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⣿⢿⡭⠟⢉⣱⣲⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠛⠛⣧⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣆⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⣀⡤⡆⣰⢟⠩⠀⠖⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠈⠀⠁⠀⢴⣩⠴⠶⡀⠀⣸⣧⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠐⠣⠤⠖⢛⠛⡛⢠⠏⠀⠄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣻⣛⣿⣙⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣀⣠⠞⠶⢷⣤⡀
⠀⠀⣠⠏⢉⣤⣴⣄⠄⣥⣿⡆
⠀⠸⠏⠿⠋⡉⠓⡴⣷⡿⠋
⣠⡤⡄⢀⠈⠛⠁⣰⣎⣉⢳⣦⣀
⠀⠀⠁⢠⡜⣖⣈⠻⢦⣄⠙⢮⣉⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢣⣼⣴⠋⣿⠟⣦⡙⡷⣆⠙⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡟⣽⣿⡿⠶⠶⠖⠀⠒⠂
⠀⠀⠀⡴⠂⠰⠻⠀⠈⠳⠈⢏⠁⡀⠙⣧⢓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃⣰⢊⡡⠄⠀⠀⠀⣀⠤⡤⠒⠒⠒⠒⢂⢤⣄
⠀⠀⡾⠁⢀⠀⠀⠀⠀⠀⠀⠘⠳⡌⠀⢨⡉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢠⠞⡡⠋⠀⠀⣠⠶⠋⠀⢀⣢⡜⠛⠉⠙⠛⠆⠀⠈⠒
⠀⢠⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠃⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡖⠁⡦⠀⠀⣠⡾⠓⠝⠋⠙⠉⠉⠉⠙⠛⠛⠳⣦⣄
⠀⣰⠂⠀⠉⠀⠀⠀⠀⣃⡀⠀⠀⣯⠀⠀⠀⠀⣜⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠂⡰⢃⣤⣚⣁⡴⣶⣲⣞⠓⡛⠛⠛⠓⠶⢦⣤⡈⣈⢷⣄
⠀⡟⠠⠂⠰⠀⠀⣶⠈⢫⠀⣖⡆⢹⡆⠀⠀⢀⠹⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣻⡿⠛⠉⠉⠈⠀⠀⠀⠀⠀⠉⠉⠒⠀⠀⠀⠈⠻⡍⠙⠻⢷⡀
⠀⢿⠀⠀⣤⣸⠀⣷⠀⠶⠀⣿⠀⠀⢻⣦⡀⠀⠳⣦⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⢮⠟⠁⠀⠀⠀⠁⠀⠀⠀⡉⠀⠐⠀⡤⠀⠀⠀⠀⠀⡰⠀⠀⠘⣷
⠀⣿⠁⠰⣿⣿⠀⢹⡇⠈⢀⢾⡀⠀⠈⠋⠻⠶⠶⠖⣛⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡡⠀⠰⠊⣉⠁⡻⠛⠀⠁⠀⠘⢞⡳⠒⢠⣀⠀⠛⠐⡀⠁⠀⠀⠀⠈
⠀⡻⠆⠚⢉⠃⠀⠀⠃⠀⠈⠀⠻⠄⠀⠀⠐⠒⠖⠲⠿⢮⣷⣶⡔⠀⠀⣀⣤⢖⢡⣚⣀⣠⣤⣀⡉⠀⠀⠈⠹⣿⠂⢄⠀⠉⠉⠄⠹⣆⠀⠘⠈⡶⠇
⢠⡇⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢩⠲⣆⠂⡀⠑⢶⣻⡉⠉⠐⣛⣒⡉⠉⠀⠀⠄⠈⠉⠁⠲⠙⠄⠠⡀⢬⡷⣄⠀⠈⠳⠈⢷⣠⠀⠀⡄
⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢠⡄⢻⠀⠙⣦⠀⠹⣧⡄⠲⢭⡯⠡⠄⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠈⠠⠁⠈⡶⡄⢀⠸⡏⠱⣆⡷⡀
⢿⣀⡳⠀⡟⢲⡀⠀⠁⠈⠤⣄⠀⠀⠀⠀⠑⠄⢳⠀⠇⠀⢸⣦⠀⡿⢶⣽⠶⣉⠐⠀⠀⠠⣀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠘⣦⠀⢹⣷⡄⣶⠀⢹⡿⠃
⢸⣇⢀⠰⣧⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⡁⠘⡇⠂⠈⡀⠀⠀⠀⠀⠈⠆⠀⠀⠒⢤⡀⠀⡀⠀⠀⠓⢎⣳⣼⠋⠉⣶⠀⠈⠁
⠀⢿⣨⡆⠙⡀⢧⡑⠢⣼⡀⠀⠐⡄⠀⠀⠀⠀⠃⠨⠀⠀⠰⡇⠀⢻⣦⠀⠘⡀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠙⣆⠘⡄⠀⠀⠀⣾⠃⠀⠀⠘
⠀⠈⢿⡟⣶⠏⢺⣷⡄⠀⠡⠄⢀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠘⡧⠀⠄⠙⠀⠀⠉⠀⠀⠀⢰⡄⠀⢠⡈⠑⣄⠀⠀⠀⢻
⠀⠀⠈⢷⡿⢀⡦⢙⣶⠄⠀⠙⣧⠀⠘⠷⡄⠀⠀⠀⠀⠆⠀⠀⠀⠈⠀⡈⠀⠆⠀⠀⠀⡀⠂⠄⠈⣿⣶⡀⢹⡉⠘⢧⠀⡾⠃
⠀⠀⠀⠀⠳⣾⣓⠈⠓⢨⣶⣦⡌⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⡌⢳⠘⠻⣷⡘⣿⣤⠄⢻⠁
⠀⠀⠀⠀⠀⠀⢻⣤⡸⠀⣄⠉⠀⠦⣀⠓⠄⢀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣸⠀⠀⠈⠙⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢁⣞⣵⠛⠆⠄⠀⠙⡂⠀⠁⠀⠤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡾⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠺⢿⣄⣀⣀⠉⠄⠠⡀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣴⣦⣄⠄⠸⡆⠀⠀⠀⠀⠀⢠⠘⠃⢸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢏⡙⠾⣆⣀⠀⠀⠀⠀⠀⠈⢀⣴⣬⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡦⢌⣉⠙⢦⣀⣄⠴⣀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠏⠹⠁⠀⠀⠉⢉⣏⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢠⠃⠀⠀⠀⠀⢸⠆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠐⠈⠓⠒⠂⠀⠀⢸⡇⠀⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠠⠴⠿⠃⣼⠄⢀⣀⡀⠀⠀⡼⠇⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢩⣿⣶⣾⣳⠞⠋⠙⠛⠋⠉⠁⠀⠀⠓⣀⢈⣳⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⣀⣀⠀⠶⠚⡖⢓⣠⡴⠊⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠚⠒⠛⡿⠛⠛⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢁⡈⣉⣈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢊⡉⢙⣛⣻⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠰⡅⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢾⣅⣬⣧⣤⣢⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠂⠡⡐⠛⣎⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠄⠀⠀⠙⢿⡥⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠆⠱⠳⢹⡄⠜⢆⠀⢣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢢⠀⢀⢣⡁⠈⣆⢀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢠⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠈⢧⠀⢆⢳⠠⣸⠦⠶⠾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠳⢆⣈⠁⠀⠀⠀⣀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣴⢌⠳⣿⣤⡂⣑⣒⣰⢖⠏⣡⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⢤⡀⢛⣚⠉⣛⠟⢩⡻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⢴⠀⣫⠐⠒⢚⣥⠬⢽⣒⢂⣰⣿⠁⠢⣤⣤⠠⣤⡄⠰⣧⣠⢿⡈⢎⣭⠹⢺⠉⠾⠤⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡟⠛⢲⣴⢞⡒⣚⡿⢆⣨⡗⠶⡧⠤⣙⣢⡚⠠⣾⡅⠘⣯⣴⣉⢽⣊⣷⢈⠗⠚⣁⠶⡤⠎⢰⡾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⢾⣏⣤⠺⠶⢮⠀⠴⠿⠶⢛⡖⣀⠯⣜⣁⣴⣉⣿⠄⠐⣾⢧⣊⣭⢴⠸⠶⡤⣤⣀⣱⣠⢳⠖⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣬⣁⡍⣷⠒⣇⣠⡶⣶⢒⡉⢛⡇⠚⠫⠀⠴⣾⠛⣲⣿⣇⡼⢏⠘⣿⣶⣤⠔⡘⢫⢁⣄⣭⡶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡆⣴⣿⡀⠘⠁⠾⣨⠛⡙⢋⠷⣾⣧⣴⣟⣩⠴⣯⣧⡐⡛⠲⣴⣏⣠⠃⡔⢻⣧⡻⡿⣧⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣏⢣⡞⢻⣇⡹⡏⣱⡹⠦⣤⢮⣄⠈⠷⠚⢛⣀⡤⢷⠆⣄⢴⡉⠹⢣⣇⡜⢰⡠⣴⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣻⣚⣻⣴⣿⣼⣌⣿⣱⢿⣿⡿⢛⣻⣿⢋⢻⣴⣾⢈⡯⢐⣯⣀⡁⢛⣴⣀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡯⣿⣉⣭⠏⢛⠿⡿⣟⠺⣉⣆⣭⣩⣄⣩⣍⣨⣷⣶⣿⣏⣤⣿⣧⡬⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⣻⣞⣽⣥⡷⢖⣯⡤⢾⣿⠌⠿⣉⣛⠧⠶⠾⠳⣿⠿⠿⣿⣿⢿⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣷⣶⣿⣭⣒⣫⡽⣉⣿⠟⣿⣿⣿⣤⢤⡦⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⡿⣿⣿⣿⣿⣿⣿⣻⣿⣽⣦⣿⣿⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡟⣯⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⣳⣿⣻⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠉⣿⣿⣿⣿⣓⣤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⠴⠒⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡉⠳⣴⠃⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠵⠀⠀⠀⠼⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⠁⠀⠀⠀⠘⢏⠉⢡⠟⠀⠀⠀⠈⠿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢷
⠀⡴⠋⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠙⢢
⡸⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⡇⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⡇⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎
⢣⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠸⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢰
⠀⢳⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⢷⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡏⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠮⣧⡀⠙⠲⢦⠤⣄⣀⣀⣀⣀⣀⣤⢴⠖⠋⢁⣾⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⠀⠀⠀⠀⠀⠀⠀⠰⠈⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⡄⠀⠀⠀⠀⠀⠀⠀⢀⠇⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢹⡘⢿⡄⠀⠀⠀⠀⠀⢀⡾⠛⡌⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣾⠁⠀⠻⠄⠀⠀⠀⠀⠞⠁⠀⢻⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡁⣿⣧⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣧⣥⣾⠫⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⣟⣽⣿⣿⣽⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⢉⣲⣦⡤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣻⢿⡼⡿⣙⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⡟⠛⠻⣿⣿⠿⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣿⣟⡿⡗⣻⡽⠷⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⢋⣤⡤⠤⠀⠈⠙⢿⣿⣿⣿⣿⡄⠀⠀⠙⢿⣧⡀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢷⡿⣷⣯⣹⣿⣹⣻⣶⠀⠀⠀⠀⠀⠀⠀⣸⡿⢁⡤⠛⡡⠴⠶⠶⠾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡶⣿⣍⣻⣷⡻⡟⣽⣾⡇⠀⠀⠀⠀⠀⠀⣿⣱⡿⣷⣼⣿⣟⠛⠓⠀⠈⠉⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣡⣟⣨⡷⢽⣖⣬⣺⡿⠿⣄⠀⠀⠀⠀⠀⣿⣾⣿⣷⡻⠞⡿⢧⡈⠶⢦⣄⣠⣸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⣿⣿⣾⣽⣿⣿⣢⣻⣿⣷⣶⣦⣴⡾⣿⡟⢻⣻⣏⢣⣿⣿⡙⡱⠦⢹⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡉⣿⢿⠶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣯⣏⢁⣪⡛⠛⡿⢿⣾⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣫⣷⣸⣶⣾⠻⢋⣿⣿⣿⣿⣷⣿⣿⣿⢿⢻⣾⣿⣿⣿⣅⣊⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣵⡿⠯⠽⣿⣿⣿⣿⣿⣿⣿⣬⢿⣿⣞⢻⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣟⢯⣛⣲⣾⣿⣿⣵⣿⣻⣿⣿⢿⣿⣯⣿⣷⡟⠛⣀⣀⡀⠀⡀⠀⡀⠀⢀⡀⣀
⠀⠀⠀⠀⣀⡀⢀⡶⠀⣀⣀⡜⠀⢀⡀⠆⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢻⣿⣿⣿⣿⣿⣿⡿⠃⠟⠛⢻⢿⣿⣿⡀⠀⠀⠀⠚⠹⢦⡀
⠀⠀⠀⠀⠙⠋⣸⠞⣡⣿⣿⣿⢿⣷⣤⡀⠈⠑⢀⠀⠙⢿⣯⣳⣽⣿⣿⣿⣿⣿⣿⣿⡯⠝⠚⠻⣿⡿⢿⡿⣋⠴⠂⠀⠹⠒⠌⠋⠻⡿⠷⠆⢦⣬⢟⣿⠢
⠀⠀⠀⠀⠀⠀⠈⠀⠘⠟⠟⠈⠃⠙⠋⠓⠀⠀⠀⠀⠀⠀⠈⢶⣹⢹⠙⣿⣿⣿⣿⣿⡿⠛⠀⠀⠈⠀⠀⠉⠁⠀⠀⠀⠀⣄⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⣧⡠⢿⠉⠉⠉⠁⠀⠀⠀⢀⠀⢀⡀⠀⠀⠴⡾⣤⣉⣻⢿⣷⣶⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⢹⣸⠀⠀⠀⠀⠀⢀⡀⠀⡠⢒⣙⡲⣤⣤⣶⣿⣛⣯⣿⣝⣿⣟⣱⠾⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⢀⣀⠀⣿⢠⡀⣴⡄⣽⣍⣉⣿⣿⣿⣿⣿⣫⢿⠿⠿⠿⠿⢿⠿⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠰⣴⣶⣶⣶⣶⣶⣤⣀⡀⠀⠀⠀⠼⠟⠛⠛⠉⠉⠁⣯⠽⠛⢋⣩⣽⣾⣿⣿⣿⡿⠿⠟⠉⠁⠀⠀⡀⠀⠐⠲⠤⠃
⠀⠀⠀⠀⠀⠀⠚⠒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡤⠀⠀⠠⠀⠀⢠⢼⣇⣤⡶⠾⠟⠛⠛⠉⠉⠙⠆⡀⠀⠦⠄⠰⠀⠀⢀⠝⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣉⣿⣿⣿⣟⣉⣁⠀⠀⠀⠈⣁⡤⠛⠛⠈⠙⠒⠀⠀⠀⠀⣀⣁⠠⢀⡀⠀⠀⠀⠀⣈⢁⣀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠉⣉⣻⡿⢟⣛⠛⠛⠉⠉⢳⣤⣀⠀⠀⠀⠁⠀⠀⡀⠀⠤⠴⠀⠀⠀⠀⠀⠂⠀⠚⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠈⠉⠁⠀⠀⠀⠀⠀⠙⠀⠀⠀⠄⠀⠀⠀⢀⡀⠂

⣤⣶⠦⢤⣤⣤⣀⣠⡶⠾⠿⠛⠿⠷⢶⣦⣄⡀
⢿⡟⣦⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣤⡀
⢸⡇⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣆
⠀⢷⠀⡈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠈⣿⠃⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆
⠀⢠⡏⠀⠀⢶⣦⣬⡙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⣸⠁⠀⣤⢸⣿⣿⣿⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠷⣶⣤⣀
⠀⣿⠀⠀⠹⣦⡙⠷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡜⠋⠀⠀⠀⠈⠙⢷⡄
⠀⣿⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⠦⠙⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⡶⠶⢶⣤⣄
⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠙⠿⣦⡀
⠀⢸⡇⣄⣀⣤⢰⡰⡖⠈⠃⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄
⠀⢸⡇⣿⣿⠙⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣧⠟⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⢸⣇⢀⣠⣤⣠⣴⣴⣴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⢀⣹⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶
⠘⣿⠘⣇⢿⢿⡻⠃⠉⠀⣷⣄⡀⠀⠀⠀⠀⢠⣀⣀⣀⣀⣠⡿⠛⠉⠉⠁⠀⣸⠿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣭⣭⡟
⠀⠹⣧⡘⢎⠳⠁⠀⠀⠀⠹⣎⠛⠶⢤⣴⠷⣤⣈⠉⠉⠉⣹⣷⠶⠶⠶⠖⠛⠁⣀⡼⠿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠁
⠀⠀⠈⢿⣎⠃⠀⠀⠀⠀⠀⠙⠷⣦⣄⣽⣄⠀⠉⠛⠛⠛⠋⠹⣷⠶⠶⠶⠶⠛⠉⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠈⠙⠳⠶⠤⠤⠴⢾⡟⠶⠦⠴⠤⠶⠖⠋⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⣄⠀⠙⠻⢶⣦⣤⣤⣤⡤⠾⠷⣤⣤⣤⣤⣤⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⣄⡙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣠⣤⣴⡶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣦⣠⣤⣤⣄⣠⠾⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠋⣠⡿⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⢀⣴⣿⣿⠟⢡⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣿⣿⣟⢶⣶⣿⣿⡿⢁⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⢿⣿⣿⡿⠿⠿⠿⠟⠁⣿⣏
⠀⠀⠀⠀⠀⠀⠠⣴⣶⣿⣛⣛⣭⣭⠅⢀⣠⣀⣠⣤⣌⣍⣟⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣟⣿⣶⠿⠟⠛⠋⠉⠁⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣰⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣭⣽⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣭⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⣿⣿⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣟⣙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠇⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⡑⠸⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⡄⠙⢆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⡟⠿⠀⠱⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣻⠻⣿⣿⣿⡿⠁⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣰⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠋⢰⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢷⠆⠛⣌⠥⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⣄⡜⢃⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠪⠒⢮⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣿⣟⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣾⡀⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠤⠤⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠴⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠤⠤⠤⠄⢀⣀⣀⠜⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠤⠄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠈⠀⠢⠊⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠉⠒⠊⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⡖⠒⠒⠂⠉⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢺⠓⠄⠀⠀⠀⠐⠹⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⢦⡔⢀⠎⠀⣤⢀⠄⠀⡱⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁⠀⠀⠀⠀⠁⠊⠀⢀⠁⠈⠀⢀⠅⡀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⠀⠀⢤⣡⠎⠀⢀⠀⠄⠀⢀⢎⠜⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⡄⠀⢀⡖⠀⠀⠀⡠⠂⠀⢀⠔⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⡃⢐⠎⠀⢀⠊⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣀⠀⠐⠀⠀⠀⠀⠁⠀⠠⠔⠁⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⡀⠀⠀⠀⡁⠀⢀⢂⠅⢄⠈⠒⠀⢠⠄⢡⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⡀⢖⠁⠄⠀⠀⠁⠀⢨⡌⠓⠃⠀⠀⠀⠈⠡⠂⠀⠀⠇⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠙⠸⠒⢁⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣀⡄⠤⢉⢀⡔⠘⠓⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠈⡀⠀⠀⣰⠆⠀⠀⢠⠀⠀⠀⠀⠀⠀⠰⡀⢉⠀⠀⠄
⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠀⢀⠄⠉⠁⠻⣚⠠⠧⠄⣄⠀⠘⢆⠀⠀⠀⠀⣀⠀⠁⠈
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠈⠄⢀⠀⡠⠇⠀⠀⠀⡁⠀⠀⢄⡀⠀⠀⠀⠉⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠴⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡇
⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠍
⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠎
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⢄⡀⣀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣿⣿⣻⣿⣿⣟⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⣠⡴⠒⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢋⠈⠃⠙⢧⣼⠃⠖⠀⠸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⣴⢯⠙⣦⡴⣞⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠀⠘⠀⢸⡇⠀⢠⠄⢀⡄⣸⢃⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣿⠄⢨⠛⠀⠆⠛⢀⡁⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⢾⡆⠓⠀⠰⠀⠑⠃⠀⠀⣠⡴⠛⢩⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣆⣄⣀⣧⣤⣃⣈⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢦⠀⡀⠰⠀⠀⢰⠄⠀⠉⠀⢠⠄⠀⣀⠀⠐⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠁⠀⠒⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⡀⠁⠀⠖⠀⡀⠀⠠⠆⠀⠀⢀⡀⠀⠀⠴⣀⡼⠁
⠀⠀⠀⠀⠀⠀⣀⣼⠃⠀⣦⣠⡦⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⣠⡴⠞⢻⣿⡟⠒⠦⣌⡁⢀⡀⠀⠆⠀⠈⠀⠰⠶⢿⡁
⠀⠀⠀⢠⣴⣾⡥⣿⠀⠀⠀⠀⠁⠀⣿⣿⠀⠈⠻⢦⣀⣀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡀⠤⠀⠈⠁⠀⠉⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠉⠙⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠋⠐⢦⣀⣉⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢤⠤⣀⣠⡴⢋⠅⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠓⠀⢸⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⡉⢋⡍⠉⠡⠄⠠⠄⠋⠭⣳⠀⠀⠀⠀⠀⠀⠀⢸⠏⠓⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠈⢧⡉⢀⠀⠦⠀⢠⠀⠰⠄⠚⠛⢦⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠰⠄⠀⢠⡀⠀⢛⣠⠞⠀⠀⠀⠀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠶⠖⠛⠉⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⡀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⠏⠉⠙⠛⢻⣛⡭⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠭⣭⣷⣴⠏⠀⠀⠀⠀⠀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠞⠉⠛⠛⠂⠀⠀⠀⢀⡼⣻⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢉⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢅⠓⢀⡘⢀⠄
⠀⡰⠁⠉⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠒⠁⢁⠈⠁
⢀⠷⠄⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⣈
⡜⠒⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠅⠀⠀⠀⠀⠀⢸⡀
⠱⡠⠀⠀⢀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠘⣆⠂⠀⠀⠀⠀⢄⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠈⠩⠋⠀⠐⠂⠀⣁⡀⣄⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⡇
⠀⠀⠀⠀⠀⡂⠀⠀⣸⡅⠤⠄⠈⠑⠤⠀⣀⠤⠤⠤⡤⠤⠤⡤⠲⠅⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⢀⠸
⠀⠀⠀⠀⠀⢨⠋⢠⠁⢀⡠⠰⠒⡀⠀⠰⢮⠁⠈⢈⡤⢴⠙⠶⠄⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠁⢀⠘
⠀⠀⠀⠀⠀⠀⡁⠀⢉⠡⠀⡀⢎⠀⡠⠐⡠⠜⡡⠁⠰⠠⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠩⣀⠠⠎⠀⠀⠉⡐⠈⠀⠚⠃⠈⠀⠀⠂⢀⠄⢠⡐⠠⠆⣀⠀⠀⠀⠀⠀⠄⠰⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠈⢠⢀⠐⠀⠪⠐⠐⠀⢀⠀⢆⠐⠙⠒⠠⠅⠀⢠⠄⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠄⠁⠀⠂⠁⠀⠀⠐⢁⣈⠀⡆⠙⠀⠙⠄⠀⠠⠁⠀⠁⠀⠀⢠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢄⣀⡠⠀⡠⠈⠁⡀⠁⠀⠀⠀⠐⠀⠄⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠂⠀⠆⣀⡁⠀⠐⠅⢠⠀⠀⠀⠀⠀⡀⠀⠀⠄⠠⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡈⠓⠇⠀⢀⠀⠀⠀⠱⠀⠈⠁⠂⠈⣠⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠠⠀⠢⢤⠠⠤⠀⠐⠋⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠑⢄⠀⠁⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠑⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠴⠀⠀⠙⠦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣴⡶⢶⣄⣴⡾⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⢿⣿⣁⣤⡽⠿⠴⠾⣥⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⢤⡀
⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⢷
⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢳⡀
⠀⠀⠀⢀⣸⡇⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇
⢀⡠⠞⠉⢸⠃⠀⠀⠀⢸⣿⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠺⠶⣤⣤⣸⡆⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⣴⠋⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠘⠛⠛⠛⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠈⠙⠒⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠛⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⢦⣄⣠⣾⣯⣵⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠉⠉⠒⠒⠲⠦⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⢶⣤⣤⣤⣴⡶⢿⡆⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⣍⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣎⣿⡛⠛⠃⠀⠀⠀⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠘⢦⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⣠⣾⠟⠈⠛⠃⠀⠀⠀⠀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣌⣳⣄⡀⠀⠀⠈⢛⣀⣀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣦⣄⣀⡀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠉⠙⠛⠛⠻⠶⠶⠿⣷⠶⠶⠶⠿⠿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣙⣻⣶⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠁⠈⣿⠀⠀⠀⠀⠀⠀⠤⠶⠶⠤⣤⣀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⢿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⢀⣤⠶⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢊⡉⢉⣛⣻⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠰⡅⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢾⣗⣬⣧⣤⣢⣝⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠂⠠⡐⠛⣎⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠄⠀⠀⠉⢿⣥⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⠱⠳⢹⡄⠜⢆⠀⢳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣢⠀⢀⢣⡡⠈⢆⢁⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠠⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⡈⢧⠈⢆⢳⠠⣸⠦⠷⠾⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠓⢆⢈⠁⢀⠀⠀⣀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣵⢄⠳⣿⣤⡂⣑⣒⣠⢖⠏⣡⢵⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣿⠤⡀⡛⣚⠉⣙⠟⢡⡻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡀⠀⢴⠀⣯⠐⠒⢚⣧⠬⢽⣚⢂⣰⣿⠀⠂⣤⣤⠠⣤⡄⠰⣧⣀⡿⡈⢄⣭⠹⢻⠉⠺⠦⢼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡟⠛⢲⣤⢞⡒⣚⡿⢳⣀⡗⠶⡧⠬⣙⣢⡚⠠⢾⡥⠘⡯⣤⣉⣼⣊⣷⢈⠖⠚⣋⠶⣤⠎⢰⠾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠈⢾⡏⣤⠺⠶⢮⠀⠴⠷⠶⢛⡖⣀⠿⣜⣁⣰⣉⣿⠄⠐⣾⢧⣎⣩⢴⠰⠾⡴⣄⣀⣱⣀⢳⠖⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⣁⡍⣷⠐⣇⣠⡶⣶⢒⡉⠛⡇⠚⠫⠀⡴⣾⠛⣲⣾⣇⡼⢯⠘⢿⣶⣤⡄⡈⢋⢁⣄⣭⡴⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡆⣴⣿⡀⠘⡁⠾⣩⠙⡙⢋⠿⣾⣧⣴⣟⣩⠴⣯⢦⡀⡻⠲⣵⣏⣠⠃⡔⢻⡧⡻⣧⢧⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣏⣡⣾⢻⣇⡹⣎⣱⡹⠾⣤⢮⣄⡉⢳⠞⢛⣁⡤⢶⡆⣄⢴⡅⠹⢣⣆⡜⢱⡠⣴⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣻⣎⣻⣤⣷⣼⣌⣿⣱⢿⣿⡿⢛⣻⣿⢋⢻⣤⣾⢈⡿⢐⣯⣀⡁⢛⣴⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣾⣿⡯⣽⣉⣭⠍⢛⠿⡿⣿⠺⢉⣆⣭⣩⣤⣩⣍⣨⣷⣶⣿⣏⣤⣿⣯⡬⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⣻⣺⣿⣥⡶⢖⣯⡤⢾⣿⠌⠿⣍⣛⠧⠴⠾⠷⣻⡿⢿⣿⡿⣯⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⣿⣷⣶⣿⣭⣒⣫⡽⣉⣿⠟⣿⣿⣿⣾⣛⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⡿⣿⣿⣿⣿⣿⣿⣻⣿⣽⣦⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡟⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣳⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡽⣳⣿⣋⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠙⠉⣻⣿⣽⣿⣓⣤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⢀⠀⠈⠡⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄
⠀⠈⠁⠀⠀⢸⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⣴⠥⠀⠰
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠠⢄⣒⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠂

⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⣆⠄⢀⠀⠀⠀⢰⠀⣰⠀⠀⠀⢰
⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠏⠾⠈⠳⠁⠼⠸⠇⠘⠠⠿⠑⠼⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⡀⡀⠀⠀⠀⡀⠀⣀⡀⠀⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠱⡀⠈⠁⣀⣼⢀⡀⠜⠀⠀⠀⠀⠀⠀⠇⢀⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠠⠀⠀⠀⠀⠀⠀⠈⠉⡋⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⣀⠄⠐⠀⢠⠀⠐⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠠
⢀⡀⠀⢰⢁⡈⢀⡶⢾⣹⡾⡿⠂⠀⠀⠄⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢐⣒⠀⠂
⠈⠻⠀⠈⠁⠠⢭⣙⣤⣄⣘⣭⡼⠶⠞⠀⠀⠀⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠐⠪⢙⠒⠀⠤⠤⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡠⠀⠀⠀⠀⠀⠀⠉⠂⠒⠒⠂⠈⠁

⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠲⣤⡀
⠀⠀⠀⡼⡩⠖⠛⠓⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⡇⠀⢻⠈⢇⡟⢲⡀
⠀⠀⢀⣟⡄⠙⢨⡇⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⡁⠀⠀⠀⡼⠀⠜⠩⢧
⠀⠀⠈⠸⡀⢳⠌⠁⠀⠀⠀⢠⣀⡙⢆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠀⠀⠀⠢⡁⠀⣀⡴⠊⣧⡀
⠀⠀⠀⠀⠉⣻⠀⠀⠀⠀⠀⠀⡉⠛⠗⠱⣄⠀⢀⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠉⢀⡤⣸⠁
⠀⠀⠀⠀⠀⡇⠀⠜⡸⠆⠓⠀⠀⡀⠀⠀⠋⢉⠉⠁⠫⠤⣀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⣨⠂
⠀⠀⠀⠀⢰⡇⠀⠶⠇⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠠⢄⠊⠀⠀⡰⠀⠀⠀⠙
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣇⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢄⠀⠀⠀⢀⠞⠀⢀⠂⠠⠤⢀⡠⢞⠀⠀⠘⣤⠋
⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢤⡀⠋⠂⢀⡡⠔⠋⠉⠁⠀⠈⠙⣶⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠚⠁⠀⠀⠀⠀⠀⠀⠂⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣦⡀⠀⠀⢠⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠆⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣀⣀⣀⠀⢠⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⢀⣠⣽⣭⠽⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣀⣀⣠⠞⠷⢴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡰⠃⠀⠀⠀⢿⡄⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁⠀⠀⣀⣀⣨⣟⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣻⠾⠉⠓⠒⠚⠂⠈⠿⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠀⠒⣶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⢠⠁⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢻⡷⠦⠤⢾⠧⢴⠚⠻⠛⠶⠤⠤⠤⢤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠠⠀⡸⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⠳⢤⡤⠃⠀⡎⠠⠀⡤⠄⠰⣄⣠⡀⠀⠙⣆⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠀⡀⣤⠔⢀⣀⢴⠾⠀⠙⠀⠓⡘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡷⡇⠘⠛⠋⡀⢀⠀⢀⠀⠀⣅⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⡼⠂⠀⠘⢛⠘⢻⡀⢋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⢀⡇⠳⡄⠀⠈⠈⠁⠉⠉⠉⠁⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠇⠙⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⡀⠀⠀⡀⠀⠀⡇⠘⢄⡀⠀⠀⡠⠻⣀⣀⡠⠏⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢄⠀⠀⠑⠢⠄⣀⠀⠀⠀⠀⣾⠈⠭⠍⠩⠍⠁⠀⡇⠀⣀⢀⢉⣉⣀⡀⠀⣀⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠠⡀⠀⠀⠀⠉⠁⠐⠾⠿⢀⣟⡀⠘⠓⠀⣠⠀⠀⢩⡄⣬⠩⠉⠁⠁⠉⠀⠀⠸
⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⣀⣀⡑⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠛⠧⠰⠴⠶⠶⠶⣦
⠀⢀⡴⠛⠛⠙⠋⠁⠉⠙⢶⣄⠀⠀⣿⠶⠛⠋⠉⠉⠉⠙⠲⢬⡒⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⡌⠀⠀⣀⣠⡀⢸
⢰⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⠷⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠉⠉⠉⠙⠂⠚⠉⠉⢀⠀⢻⠋⠀⠀⠈⢋⣉⡡⠼
⡏⠀⠀⠀⠀⣰⠋⠉⠙⢳⣶⡿⠘⠁⠀⣠⠖⠓⠉⠙⢦⡀⠀⢀⣀⡿⠷⠤⠴⠆⠀⠲⠒⠴⠶⠦⠤⢤⣴⡟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⡀
⠃⠀⠀⠀⠀⠇⠀⠰⠊⣸⡏⠀⠀⠀⠀⠻⣀⡀⣀⡤⠞⠋⠉⠀⠀⢀⣀⣀⠤⠤⠤⠤⠤⠄⣀⣀⡀⠀⠀⠉⠙⠒⠤⣀⠀⠀⠀⢀⡴⣋⡿⠷⢦⡀
⠰⡄⠀⠀⠀⠈⠓⠲⠟⠛⢧⠀⠀⠀⠀⠀⡼⠛⠁⠀⣀⡤⠖⠊⠉⢈⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠉⠒⠦⢄⡀⠀⠀⠑⠢⣴⣩⡟⣹⠤⠖⣶⠟⢧⣀
⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⢀⡷⢦⣀⡰⠋⠀⠀⡠⠊⡥⢤⣀⡔⠊⠉⠙⣿⠯⢤⣞⣿⡾⣻⣏⢉⡵⣶⢦⣀⠀⠉⠒⣄⠀⠀⠈⠻⣿⡧⣶⠋⢉⣽⠛⢯⣧
⠀⠀⠀⠀⠉⠑⠒⠒⠒⠚⠉⠀⠀⡟⠀⠀⢀⠞⠀⢀⡴⠾⠿⡆⠀⠀⣴⠃⠀⢠⠋⠉⠉⢉⠏⠀⠀⠘⡟⠋⠑⢦⠀⠀⢳⡀⠀⠀⠹⣿⣛⣻⣋⣉⣩⠟⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡎⠀⣰⢻⠀⠀⠀⣸⣏⣉⣽⣇⡴⡞⠀⢀⡰⠛⢳⡤⡤⣾⠥⠤⢄⡠⢳⡄⠀⢷⠀⠀⠀⢋⣸⣏⣋⡽⠉⠙⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡇⢠⣏⠙⠤⡤⠴⠛⠌⢻⡶⣏⠀⠈⠉⣁⣹⣀⣸⣄⠑⣷⠀⠀⠘⡷⠋⡿⣄⢸⠀⠀⠀⢸⣇⣀⣝⠹⢓⡶⠧⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢯⠹⡏⠹⢶⣿⣻⣦⠀⣀⣽⠛⢋⣩⣿⣏⣿⢯⢤⠀⣑⡛⡶⡖⣾⣁⣼⣾⣇⡎⠀⠀⠀⣾⣻⣏⡉⣹⢿⢦⣤⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣀⣀⣈⣿⣷⡧⠴⢟⡛⣛⣉⠉⣉⡀⠘⠻⠾⠀⠈⠁⣼⣼⣭⡟⠓⢻⣁⠀⠀⣸⠟⠀⠀⠀⣼⠉⠑⣴⡙⠙⢳⣾⣁⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠉⢉⣩⢭⣭⣵⠶⠒⠛⢿⣍⠁⢽⠁⠀⠈⠛⡿⠟⠉⠒⠒⠚⡄⠀⠀⣷⠤⠿⣯⡷⠛⠁⠀⠀⣠⣞⠛⢳⢶⠋⢉⠟⢧⣀⡝⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠒⢄⡀⠀⠈⠑⠂⠕⣶⣿⠞⢣⣜⠄⠒⠒⢲⣧⣄⡴⠥⠔⠊⠁⠀⢀⣠⣴⠿⡁⢈⠷⣅⢀⡽⠧⢤⣀⠟⠦⣤⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠄⠀⣀⠀⠀⠀⠀⠉⠈⠁⠉⠀⠀⠀⢀⣀⠠⠤⠒⢊⠉⠉⠑⣤⡜⢧⣀⣼⢋⠛⢣⡴⠛⣆⡠⠊⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠒⠒⠀⠉⠉⣁⡀⠀⠀⠀⢮⣋⠆⠀⠈⠣⣤⣏⡽⣻⡔⠛⢧⡠⠚⢷⡤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⣈⡼⢟⠻⢳⠀⣡⠦⡄⠀⠀⠀⠀⠟⠉⣀⡡⠋⠉⢳⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣩⠟⠓⠋⠉⠁⠀⠛⠴⠀⠀⠀⠀⠀⠱⣴⠿⠧⣄⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣦⣼⣆⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⣤⠦⠉⠛⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡈⢀⠎⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡮⢭⣤⡄⠀⠸⣨⠇⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⢀⠊⢠⢀⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣧⠏⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡏⣰⠃⡜⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠠⠀⠜⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠠⠀⠰⠦⠂⠺⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⢀⡴⣃⣀⠀⠠⠴⠖⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⢠⣀⠀⠀⠀⠀⠀⠙⠢⢤⣤⣴⠖⠋⠁⠉⠉⠁⠀⠀⠀⡀⠀⢄⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⢠⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠁⠠⢀⠀⠀⠢⣀⠀⠈⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⡀⠀⠁⠐⠆⠀⠀⠀⠀⠐⠀⢰⠀⠁⠚⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠈⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⠀⠀⠀⠀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠒⠀⠀⢀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⢠⡀⠀⠐⠀⣀⡁⠀⠈⠲⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠉⠉⠈⠀⠀⠀⠀⠀⠈⠈⠁⠉⠀⠉⠂⠉⠊⠉⠀⠁⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣭⠀⠲⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⡠⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⠓⠂⣤⣀⠀⠀⠀⠐⠀⠀⠀⣄⣤⡦⠁⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠈⢑⣵⡾⠣⣤⡀⠀⠀⠀⠀⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⢛⡟⠀⠀⠀⠀⠉⠓⠲⠤⡴⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢐⣠⠳⠙⣇⡤⠄⠄⠀⠒⠊⠥⠤⠍⣉⢠⣿⡄⠨⡷⠆⠰⠭⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠾⠟⢁⣟⠉⠛⠂⠉⠁⠀⠀⠀⠀⡀⠩⢄⣈⠸⠥⠒⠶⣈⠉⠁⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⢒⣩⡤⠄⣀⠔⠀⢀⣀⣀⠀⠀⠲⠖⠒⠊⠑⠂⠈⠀⠀⢂⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣧⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠯⢾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣰⠻⠀⠀⠀⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢄⢽⣟⠉
⠀⠀⠀⠀⠀⠀⢐⣿⡃⠀⠐⠀⢀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠦⣽⣃⡘⣯
⠀⠀⠀⠀⠀⠀⢸⢓⠁⠀⡀⠘⠋⡉⠰⡆⡀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣿⣿⡿⠰⡙
⠀⠀⠀⠀⠀⠀⢸⢾⡀⠀⠋⠀⠸⠅⠀⣠⢤⣔⢀⠠⠤⠄⠐⠺⢝⣸⡯⣩⠁⠂⡀⢧
⠀⠀⠀⠀⠀⠀⠰⣧⣤⢉⠠⠀⠈⠲⠂⢩⠖⠀⠚⠉⣉⡀⠠⢆⣿⣫⣾⡏⠟⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠙⣾⣯⢤⠶⣀⠶⠒⠋⡠⠀⢠⠂⣈⠀⠠⠂⠈⡉⡹⡅⠁⠀⠄⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣠⣤⣶⡄⡁⣄⣰⡀⠗⠀⢘⣀⣮⢟⠽⠀⢃⠠⠎⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣼⣟⣶⣿⠿⠒⣶⣹⡤⣶⡧⢼⡥⣟⣷⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣯⡝⣻⣏⠁⢀⡙⡻⢆⣰⣿⣿⣗⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣽⣿⠻⣦⣦⣽⣟⣻⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⢿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⢺⡆⠥⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⢋⣍⢉⡉⠓⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⣀⣠⣤⣤⣀⡀⠀⠈⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⡴⣫⣅⢄⣰⠠⠈⠝⢦⡀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⡞⢼⣊⠊⠜⠇⠁⠈⠁⠦⢹⡀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠓⠱⡠⠁⡅⠂⡀⠀⠈⢠⠷⠶⣄⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠉⠉⠉⠉⠉⠉⠉⠙⠓⠲⠤⣄⡀⠀⠀⠀⣇⠀⠀⠀⢳⡄⠔⠈⣈⢄⠐⠊⠌⣀⣼⠟⠛⠁⡞
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⣀⣤⠤⠴⠶⠶⣶⣶⣶⣤⣄⣀⠀⠀⠉⠒⢤⡀⢸⣄⠀⠀⠀⠙⠶⣼⣂⡪⣁⣮⡵⠛⠁⠀⠀⣰⠃
⠀⠀⠀⠀⠀⡠⠊⠁⠀⢀⣤⣶⣿⡛⠓⢦⣤⡄⠸⣷⢄⠐⢈⢻⡈⠙⠲⣄⠀⠘⢉⡻⣿⣦⡀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⢀⡴⠃
⠀⠀⠀⣠⠊⠀⠀⣠⣶⡏⠀⣹⠛⠻⠶⢿⣤⡇⠀⠙⢮⡧⠄⠁⠑⢦⡀⠀⠙⢦⡈⠁⠈⢻⣿⡶⢄⣀⡀⠰⠆⠖⠀⣀⣠⠔⠋
⠀⠀⡴⠁⠀⢀⣼⠿⣽⡧⢤⣿⠦⣦⡄⢀⡍⠛⢓⢆⠈⢷⡂⢡⡀⠠⠙⡆⠀⠀⠑⣄⠀⠀⠹⡇⠀⠈⠉⠉⠉⠉⠉⠁
⠀⡸⠁⠀⢠⡏⣸⣠⡇⢀⣠⡃⢀⣼⣽⣷⠲⡀⠄⠉⠛⠶⣿⣿⣬⡤⠀⢹⣦⡀⠀⠘⣆⠀⠀⠹⡀
⢰⠃⠀⢀⣿⣧⠋⠉⣹⠁⠀⣿⣏⠀⣼⣃⠀⠈⠻⢧⣙⣶⢤⡘⠻⢦⡀⠀⠀⠻⡄⠀⠘⣆⠀⠀⢧⠀⠀⠀⠀⣀⡤⠔⠒⠋⠉⠉⠉⠉⠓⠒⠤⣄
⡾⠀⠀⣸⡿⠻⣤⠼⢻⠶⠚⠋⠉⠉⠙⠛⠛⠦⢤⣀⠀⠉⠛⢿⣴⠄⣗⠄⠒⠀⢹⣄⣀⣿⠀⠀⠸⣄⣀⡴⣪⠅⠀⠀⣀⣀⣤⠴⠚⠉⣹⠀⢠⠶⡝⠦⡀
⡇⠀⠀⣿⣇⡀⣸⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣠⠄⠈⠙⠶⣽⣦⡂⡄⠀⠳⡽⠟⢦⡀⠀⡿⠋⠘⠁⣠⠖⢋⡽⠋⠁⠀⠀⢠⠟⢿⠏⠀⢹⠀⠈⢦
⡇⠀⠀⣿⠉⢿⠋⠀⠀⠀⠀⣠⠴⠖⠒⠒⢦⠀⠀⠂⢸⡙⠂⠀⠀⠀⠀⠈⢷⡘⡆⠀⢻⣿⣫⠇⠀⡇⠀⣠⣾⡵⠚⠁⠀⠀⠀⠀⢀⠏⢠⠏⠀⠀⠸⡇⠀⠀⢳
⢷⠀⠀⢿⠙⣿⡀⠀⠀⠀⡾⢱⠀⠀⠄⢂⢘⣇⡴⠒⠚⡛⠛⠉⠓⢦⠀⠀⠀⢹⡄⠠⠀⣿⠃⠀⢰⠁⢸⡟⠁⠀⠀⠀⠀⠀⠀⢀⡎⢀⠏⠀⠀⠀⠀⣷⡀
⠸⡄⠀⠸⡇⠜⣧⠀⠀⠀⢷⡈⠀⡀⠆⢀⣸⠟⢀⡤⠥⠦⣤⡀⠀⠀⢳⣀⠀⠸⣌⣅⣠⡟⠀⠀⡜⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⡼⢀⡞⠀⠀⠀⠀⠀⢹⣇
⠀⢱⡀⠀⠙⣦⣈⣦⡀⠀⠀⠈⠓⢳⡿⠛⠁⣰⠯⡀⠀⠐⠠⠙⣆⠀⠀⢹⣆⠂⡈⣹⠟⠀⠀⣰⠁⠘⣯⣿⣇⠀⠀⠀⠀⠀⡜⢁⡜⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⢳⡀⠀⠘⢖⡐⡛⡄⠀⠀⠀⢸⠀⠀⠀⢿⡣⠐⠠⠐⢀⠂⡿⠀⠀⠈⢷⣬⣶⠋⠀⠀⣰⣷⠀⠀⢹⣽⣿⡀⠀⠀⠀⣰⢗⡾⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠙⢄⢀⡈⠳⣄⠿⢦⣀⣀⣼⣧⠀⠀⠈⠳⣤⣁⣵⣥⠖⠁⠀⠀⠀⠈⢿⠁⠀⢀⠞⠁⠙⡆⠀⠀⢻⣷⣹⡄⠀⢰⡏⡼⠁⠀⠀⠀⠀⠀⠀⢀⣤⠏⠀⢰
⠀⠀⠀⠀⠀⠻⢵⡆⠈⠑⠦⣈⠉⠀⠈⠣⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡞⣀⠔⠁⠀⠀⠀⠘⢆⠀⠀⠙⣧⣇⢠⣯⣥⠃⠀⠀⣀⣀⣠⣴⡾⠟⡡⠆⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠉⠑⠲⠤⠶⢭⣽⠷⠶⠶⠦⠤⠤⠖⠊⣉⡥⠒⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠘⠿⠿⢾⣷⣶⣶⣿⠧⠴⠚⠉⠀⠀⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⢤⣀⣀⣀⣀⣀⣀⣀⣠⠤⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⣀⠀⠈⠁⠀⠀⠀⠀⣀⣠⠔⠊⠁

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢰⠁⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠢⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⢆⠀⠀⠀⠐⠠⠀⠀⠄⠂⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠰
⠀⠀⠀⠀⠀⠈⠐⠀⠀⠄⠀⠀⠠⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠐⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠠⠲⠀⠂⠀⠄⢠⠄⠂⠊⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣊⠠⠁⠀⠀⠀⠐⢘⠀⠀⠀⠀⠀⠈⠁⠀⠀⠄⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠡⢉⠀⢀⡀⠀⠀⠀⡀⠈⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡈⠀⠆⡈⠂⠄⡁⠀⢔⠀⡑⠀⡐⡂⠘⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠈⠒⢄
⠀⠀⠀⠈⡄⣆⢱⠀⠀⠀⠀⠀⠀⡄⠁⠀⢠⠀⠈⠀⠈⠚⠋⠄⠉⢉⠁⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠃⢱⠘⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠂⠐⠃⠀⠚⠉⠉⠉⡉⠉⠉⠉⠐⠀⠀⠄⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠈⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠐⠀⠀⠌⠀⠀⠀⠊⠀⠀⠀⢀⣀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠄⠤⠒⠂⠀⠀⢠⠏⠉⠉⡁⠀⠀⠀⠠⠀⠈⠉⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡘⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢶⠰⠀⠒⠂⢀⣶⠚⠈⠉⠉⠉⠉⠉⠉⠂⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⠀⠀⡞⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠂⠠⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢷⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⠤⠠⠬⠙⠶⠤⠤⠤⠤⠤⠤⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠒⠲⣦⡞⠁⠀⠀⠀⠀⠙⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⢀⡿⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠉⢳⡄⣠⠞⠋⠉⠉⠁⠘⠓⠲⢤⣀⠀⠴⠋⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣸⠇
⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏
⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣠⣤⡀⠀⠀⣠⠴⠶⢦⣄⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢀⣾⣆
⠀⠀⠀⠀⠀⠀⡿⠀⠀⢸⣿⣧⣿⠀⢸⠃⠀⠀⠀⢹⡆⠀⢾⣿⣦⣿⠀⠀⠀⠀⠀⠀⠀⢸⡟⣩⠏⣹
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠉⠋⠁⠀⠘⢧⡀⠀⣠⠜⠁⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⡴⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⢀⡟⠀⠉⣰⠏
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢾⡁⣠⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢦⣀⣙⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢦⠀⠀⢈⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣬⣽⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⣦⣄⣀⡀⠀⠀⠀⠀⣀⣀⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠾⠶⠧⣭⡉⠛⠛⠛⢛⣩⠽⠿⠶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⡴⢦⠀⠀⡞⢶⡙⣦⠀⢰⢋⡴⢲⡄⠀⡴⢦⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠁⠀⠙⠁⠀⠈⠋⠁⠈⠓⠞⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣟⣻⣿⣫⡭⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠿⣍⣶⣄⠀⠀⠀⠀⠀⠀⢀⣠⡶⢿⣽⠏⠿⣽⣿⠷⣿⣻⣟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠶⠾⢋⡥⠾⣳⣄⣠⣤⣤⣴⣫⠩⠰⣕⣯⣶⡦⣵⡿⢿⣿⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡞⣨⢔⣫⣽⣿⣿⣿⣿⣿⣿⣵⣮⣿⡏⡿⣳⢖⣛⣻⡯⣟⡟⡪⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣰⣯⣾⣵⣿⣿⣿⣿⢿⣿⣿⣿⡿⣷⣼⣿⣫⢤⣶⣿⡻⢳⣽⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⣯⣿⣿⣿⣿⣽⣟⣒⣿⢿⣟⣫⣑⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡝⣿⣿⣿⣿⣿⣿⣿⡶⣲⣾⣿⣿⣷⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣏⣾⡿⢿⣿⣿⣻⣿⣵⣿⣿⣽⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣻⣗⣽⠿⣿⣿⠿⣻⣿⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⣿⣿⣿⣯⣿⢿⣿⣾⣿⣽⡻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣾⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⣿⢸⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠈⢶⠙⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠢⣼⠋⠓⠒⠂



⣿⣿⣿⣻⣟⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣟⣛⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠿⢰⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠐⠂⢠⡑⠎⣡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠉⠀⠀⠐⠀⠀⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⡆⠀⠀⠀⠀⠀⠀⣀⠁⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⣉⣿⡃⠀⢴⣶⣶⠁⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣾⣿⡇⢈⣁⡄⠀⢿⡀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⠟⠀⢻⣿⣿⣇⠈⣿⠆
⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡏⢶⠖⢻⣿⠛⣿⡟⢻
⠀⠀⢀⣀⣀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠾⠧⣁⢀⡐⠃⢿⡧⣄⠐⢉⣶
⠀⠀⠣⢈⡁⠠⠄⠀⠀⠀⡀⠀⠰⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠰⠆⠉⠘⡷⠗⡶⢀⠙⠛⠈⣋⠃
⠀⠀⠀⢰⠇⠀⠠⠶⠄⠀⣭⣀⡀⠙⠶⢅⣛⠂⣐⠰⠂⠀⣤⣤⣀⣀⢀⣠⣄⠀⠀⠰⠀⠀⠀⠇⠀⠣⠀⢀⠁⠘⠧⡤⡤⠀⢠⣄
⠀⠀⠀⠈⠀⠀⠲⠒⠀⠲⣀⡀⠈⠁⣄⠀⡀⠀⠈⢘⢂⡈⢹⣤⣛⢛⣦⠛⠡⣤⢀⠀⣰⠈⠄⢠⠀⡼⠀⠈⠳⠄⠠⠂⠁⠐⣾⡇
⠀⠀⠀⠀⠀⠀⢰⣤⠄⠊⠨⣑⡉⣄⠀⠂⢁⡠⣷⣶⢞⡡⣤⠄⠃⠘⠅⠟⠠⠂⢙⢠⠏⠠⡆⢸⡖⢰⠁⠀⠀⡄⠀⠐⠰⡾⠟⡹⡀
⠀⠀⠀⠀⠀⠀⠳⠃⠀⠐⠒⡎⠱⢤⣧⠔⣯⠁⠮⢠⡏⣘⡿⢶⡀⠈⠚⣹⠃⢉⣉⣁⡸⠀⠿⠾⠠⠈⠄⢐⠈⢡⡴⠀⠰⠙⠂⡃⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣯⡽⠞⣡⡄⣸⣿⣸⡦⢾⠷⢉⣽⠾⡝⠩⣼⠋⡙⠃⠀⢁⡀⠀⢀⠀⠀⠈⡀⣡⠼⠀⢠⡘⢇⣠⣂⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠉⠤⠁⠚⣷⣾⠿⣿⠟⢀⡴⢛⣓⠿⢀⡄⠡⠄⣉⠈⠁⠛⢀⣀⡠⡀⣀⠄⠉⠀⠀⠘⠏⣤⠸⡇⠱⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠫⣤⣴⢓⣷⠛⣇⣿⡍⣁⣤⣤⣆⣈⠩⡖⢫⣧⣤⡉⢄⣤⠾⢤⡖⢀⠲⠁⠚⠁⢒⣸⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⣀⣿⡶⠚⠋⠈⠠⠾⡛⠻⢿⣿⣾⣿⡟⣋⠙⠳⣤⣰⢭⣿⡿⢿⠙⠁⠰⠗⢸⠇⣤⣄⣸⢎⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠹⢿⡟⠂⠀⢀⡌⢀⠉⠂⠀⠉⠉⠉⠙⠉⠑⠛⡍⠙⠂⢤⢀⡉⠳⠀⠐⠠⡖⢂⠇⠨⢭⡟⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠴⠂⠀⠀⣽⠉⠁⠤⠕⠀⠔⠃⢐⡀⠁⠀⠀⢀⣠⣤⣤⣁⣠⣉⣀⡀⣀⣁⣸⣀⣀⣸⣼⣧⣤⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣀⠉⠀⠙⢁⡄⠀⠈⠅⠂⠘⠦⠶⠉⠁⠀⠁⣉⣉⣉⠉⣍⣹⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⠙⢋⣭⣤⡎⠀⠀⠀⡠⠀⠈⠶⡦⢘⣛⡋⣀⣟⡉⡛⢛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠤⣫⣄⠚⠃⣮⢤⣌⣸⠊⢛⣿⠿⠻⣿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢀⡿⣿⣵⢋⠸⣿⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡄⣿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡷⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣫⣭⡽⢿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣶⣿⣿⠿⣥⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠶⠚⢓⣾⣿⣟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣭⣿⣿⣿⣿⣾⡃⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⣴⡚⣛⣳⣿⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣤⣃⢠⡐⣓⣠⣤⣤⣄⣀⣀⣀⣤⠆⢠⢤⣄⡈⡀⠴⠚⠁⣸⣏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣛⠕⠚⠁⣐⠆⣨⠉⢙⡿⢿⡉⠀⠀⠀⡙⠰⢏⣱⡄⠛⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⡿⡟⢫⣰⢠⣌⡇⡁⡈⢶⣌⡀⠈⠧⣅⣀⣰⡟⣙⣯⠀⠀⠀⠀⢐⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣍⡧⣞⣻⢼⣻⡼⢧⢿⡀⣺⣿⣷⣶⣞⡣⢬⡏⠠⠾⠤⢤⣀⣀⣲⣾⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣳⣯⣷⢺⢬⣗⣻⣚⣣⠼⠛⠻⣿⣯⣥⣀⣀⣘⣺⣴⣶⣶⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣷⠟⣿⠖⠼⡭⢏⣉⡶⢾⡉⣁⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⣿⣮⣿⣳⡞⣯⣽⠛⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣷⢻⣤⣿⡻⣿⢿⠷⣽⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡿⢿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣠⣠⣾⣦⣤⣀⣄⣀⣠⣄⣠⢂⡜⣸⣎⣴⣮⣤⣄⠀⠀⢀⣠⣀⢀⡀⢀
⠀⠀⠀⠀⠀⡰⣰⣶⣢⣶⡴⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣟⣛⣻⣿⠟⢡⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣯⣖⣩⣿⣶⣤⣶⣦⠆
⠀⠀⠀⠀⠀⠃⠃⠃⠋⠛⠙⠛⠋⠙⠽⠿⠫⠾⠿⡿⢿⠿⢯⣿⢗⣢⣿⣿⠟⠉⠘⡿⠫⠽⠻⠾⠛⠉⠉⠉⠈⠉⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢉⡄⢨⡝⠽⠧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠈⢣⡱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠸⣧⣵⡷⢶⣵⠾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢉⣀⢢⡉⠱⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠂⠀⠀⠀⠹⡷⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢉⠀⠉⢃⢣⠘⡙⠆⠘⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡁⠂⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⢆⠀⡌⢧⠂⠸⡄⢀⢺⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢁⠂⡄⢀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⢧⣸⠎⢃⢶⣛⡛⡉⣻⠗⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⢦⢀⡤⣤⣄⡴⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡘⠋⠀⡙⢷⠇⣐⣒⡶⠣⠭⣐⡙⢃⣤⠄⡀⠀⠀⠀⠀⠀⣠⠘⠻⡏⢷⢴⢼⡄⡴⢉⡘⢫⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢤⣘⡃⣘⣇⣀⣴⣟⠨⣝⣐⣖⠺⢿⡀⡌⠛⣻⠝⢿⡆⡘⠗⣞⢷⡈⢞⣂⡵⣇⡈⣹⠉⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠙⢠⣤⠟⢁⣆⣰⠊⢐⣾⣃⣭⣏⠡⣶⠺⠂⣩⠻⣧⠈⣙⣷⢊⠷⠎⠅⣏⡄⡐⠉⢿⠁⣌⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠟⠺⢧⡉⡽⠁⣉⣩⣅⠔⢳⣖⣩⡗⠒⣻⣿⡏⣤⣴⠋⣿⠞⢯⣥⣉⠉⠙⡿⠞⠛⠖⢣⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣏⢈⣡⠚⠚⠏⣹⠐⡦⠴⠦⣦⣤⡊⣩⡿⠒⣹⢛⡉⠡⢧⡜⣹⠛⡩⢈⠼⣆⣷⣟⡇⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣾⣿⢿⣠⢶⡅⢹⡄⢣⢾⣤⣉⡝⠙⢳⣏⡼⠯⢉⣢⣥⢝⢋⡞⠣⣎⡄⢩⢪⣉⣘⣧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⡭⢶⣉⣷⣱⡙⡧⢥⣿⣿⣷⠶⣦⡶⠿⣏⣠⡏⢺⡃⣵⡀⠘⠿⣇⠜⣡⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⡿⣿⣻⠟⣛⡛⢿⣿⣿⣿⣽⣯⣵⣚⣛⣱⣒⡟⣻⣧⣿⣶⣋⣷⣿⣐⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡷⣾⣏⣭⠤⣾⣫⠙⢋⠛⠿⠿⠿⠯⠹⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣾⣿⣷⣬⣡⠄⣠⣄⣄⣹⢤⣽⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣿⣿⣿⣱⣯⣏⣉⣀⣩⣽⡟⢏⣉⡉⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣷⣿⣡⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⣿⡿⠿⣿⣶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁